From 8a5a24c5cb6cd9f95494685719ef2b77cadede33 Mon Sep 17 00:00:00 2001 From: S-Explorer <1246206018@qq.com> Date: Mon, 28 Apr 2025 21:32:06 +0800 Subject: [PATCH] docs:add IAMReX documentation --- .github/workflows/docs.yaml | 38 + Docs/IAMReX_documentation/Makefile | 20 + Docs/IAMReX_documentation/make.bat | 35 + .../source/Acknowledgements.rst | 6 + .../source/GettingStarted/IAMR_LSAMR.png | Bin 0 -> 140061 bytes .../source/GettingStarted/Monodisperse.png | Bin 0 -> 78572 bytes .../source/GettingStarted/RSV.jpeg | Bin 0 -> 80370 bytes .../source/GettingStarted/RT_tip.png | Bin 0 -> 41748 bytes .../source/Getting_Started.rst | 443 +++++ .../source/Introduction_Chapter.rst | 46 + Docs/IAMReX_documentation/source/Results.rst | 80 + .../source/Results/FlowPastSphere.png | Bin 0 -> 66037 bytes .../source/Results/FlowPastSphereResult.png | Bin 0 -> 30993 bytes .../source/Results/MonodispersPDrop.png | Bin 0 -> 41320 bytes .../source/Results/MonodispersSliceResult.png | Bin 0 -> 229081 bytes .../Results/MonodisperseParticlesAMR.png | Bin 0 -> 572038 bytes Docs/IAMReX_documentation/source/conf.py | 43 + Docs/IAMReX_documentation/source/index.rst | 23 + .../source/references.rst | 7 + Docs/IAMReX_documentation/source/refs.bib | 1437 +++++++++++++++++ 20 files changed, 2178 insertions(+) create mode 100644 .github/workflows/docs.yaml create mode 100644 Docs/IAMReX_documentation/Makefile create mode 100644 Docs/IAMReX_documentation/make.bat create mode 100644 Docs/IAMReX_documentation/source/Acknowledgements.rst create mode 100644 Docs/IAMReX_documentation/source/GettingStarted/IAMR_LSAMR.png create mode 100644 Docs/IAMReX_documentation/source/GettingStarted/Monodisperse.png create mode 100644 Docs/IAMReX_documentation/source/GettingStarted/RSV.jpeg create mode 100644 Docs/IAMReX_documentation/source/GettingStarted/RT_tip.png create mode 100644 Docs/IAMReX_documentation/source/Getting_Started.rst create mode 100644 Docs/IAMReX_documentation/source/Introduction_Chapter.rst create mode 100644 Docs/IAMReX_documentation/source/Results.rst create mode 100644 Docs/IAMReX_documentation/source/Results/FlowPastSphere.png create mode 100644 Docs/IAMReX_documentation/source/Results/FlowPastSphereResult.png create mode 100644 Docs/IAMReX_documentation/source/Results/MonodispersPDrop.png create mode 100644 Docs/IAMReX_documentation/source/Results/MonodispersSliceResult.png create mode 100644 Docs/IAMReX_documentation/source/Results/MonodisperseParticlesAMR.png create mode 100644 Docs/IAMReX_documentation/source/conf.py create mode 100644 Docs/IAMReX_documentation/source/index.rst create mode 100644 Docs/IAMReX_documentation/source/references.rst create mode 100644 Docs/IAMReX_documentation/source/refs.bib diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml new file mode 100644 index 00000000..517a6493 --- /dev/null +++ b/.github/workflows/docs.yaml @@ -0,0 +1,38 @@ +name: Build and Deploy +on: + push: + paths: + - 'Docs/IAMReX_documentation/source/**' + - '.github/workflows/docs.yaml' + +concurrency: + group: ${{ github.head_ref }}-docs + cancel-in-progress: true + +jobs: + build-and-deploy: + runs-on: ubuntu-22.04 + steps: + - name: Checkout + uses: actions/checkout@v4 + + - name: Dependencies + run: | + echo "Installing python packages for docs..." + python3 -m pip install --upgrade pip + python3 -m pip install sphinx sphinx_rtd_theme breathe sphinxcontrib.bibtex docutils + + - name: Install and Build + run: | + echo "Build the Sphinx documentation for IAMR." + make html + + - name: Deploy + if: github.event_name == 'push' && github.repository == 'ruohai0925/IAMReX' && github.ref == 'refs/heads/development' + uses: JamesIves/github-pages-deploy-action@v4 + with: + ssh-key: ${{ secrets.DEPLOY_KEY }} # repo secrets env + branch: gh-pages # The branch the action should deploy to. + folder: build/html # The folder the action should deploy. + target-folder: docs # The folder the action should deploy to. + clean: false # Do not remove existing files from the deploy target. diff --git a/Docs/IAMReX_documentation/Makefile b/Docs/IAMReX_documentation/Makefile new file mode 100644 index 00000000..d0c3cbf1 --- /dev/null +++ b/Docs/IAMReX_documentation/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/Docs/IAMReX_documentation/make.bat b/Docs/IAMReX_documentation/make.bat new file mode 100644 index 00000000..dc1312ab --- /dev/null +++ b/Docs/IAMReX_documentation/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.https://www.sphinx-doc.org/ + exit /b 1 +) + +if "%1" == "" goto help + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/Docs/IAMReX_documentation/source/Acknowledgements.rst b/Docs/IAMReX_documentation/source/Acknowledgements.rst new file mode 100644 index 00000000..173dd833 --- /dev/null +++ b/Docs/IAMReX_documentation/source/Acknowledgements.rst @@ -0,0 +1,6 @@ +.. _Chap:Acknowledgements: + +Acknowledgements +================= + +We are grateful to Ann Almgren, Andy Nonaka, Andrew Myers, Axel Huebl, and Weiqun Zhang in the Lawrence Berkeley National Laboratory (LBNL) for their discussions related to `AMReX `_ and `IAMR `_. 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z>cftcUAP*)=IwrhTEe=a@ElEYA~MKuhk1sFQ}b2WP@UJb_3p%)z_iBD(&pLV?~%{d oo-WAWF8ld6i>m(9-OMc6#J~0v$IQ%s+W70f$oxNM_fP(R0Eay)j{pDw literal 0 HcmV?d00001 diff --git a/Docs/IAMReX_documentation/source/conf.py b/Docs/IAMReX_documentation/source/conf.py new file mode 100644 index 00000000..f82c22b4 --- /dev/null +++ b/Docs/IAMReX_documentation/source/conf.py @@ -0,0 +1,43 @@ +# Configuration file for the Sphinx documentation builder. +# +# For the full list of built-in configuration values, see the documentation: +# https://www.sphinx-doc.org/en/master/usage/configuration.html + +# -- Project information ----------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information + +import sphinx_rtd_theme + +project = 'IAMReX' +copyright = '2025, IAMReX' +author = 'YD Z' +release = '0.1.0' + +bibtex_bibfiles = ["refs.bib"] +source_suffix = { + '.rst': 'restructuredtext', + '.txt': 'markdown', + '.md': 'markdown', +} +main_doc = 'index' + +# -- General configuration --------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration + +extensions = ['sphinx.ext.mathjax', + 'sphinxcontrib.bibtex', + 'sphinx.ext.githubpages', + 'sphinx.ext.viewcode', + 'sphinx.ext.intersphinx', + 'sphinx.ext.autosectionlabel' + ] + +templates_path = ['_templates'] +exclude_patterns = [] + + +# -- Options for HTML output ------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#options-for-html-output + +html_theme = 'sphinx_rtd_theme' +html_static_path = ['_static'] diff --git a/Docs/IAMReX_documentation/source/index.rst b/Docs/IAMReX_documentation/source/index.rst new file mode 100644 index 00000000..6fd5d678 --- /dev/null +++ b/Docs/IAMReX_documentation/source/index.rst @@ -0,0 +1,23 @@ +.. IAMReX documentation master file, created by + sphinx-quickstart on Sun Apr 27 13:57:52 2025. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +IAMReX documentation +==================== + +This IAMReX repo extends the capability of original `IAMR `_ codes, aiming at simulating the multiphase incompressible flows and fluid structure interaction problems on both CPUs and GPUs with/without subcycling. The Navier-Stokes euqations are solved on an adaptive semi-staggered grid using the projection method. The gas-liquid interface is captured using the level set (LS) method. The fluid-solid interface is resolved using the multidirect forcing immersed boundary method (IBM). The particle-wall as well as the particle-particle collisions are also captured by the adaptive collision time model (ACTM). + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + + Introduction_Chapter + Getting_Started + Results + Acknowledgements + +.. toctree:: + :caption: References: + + references diff --git a/Docs/IAMReX_documentation/source/references.rst b/Docs/IAMReX_documentation/source/references.rst new file mode 100644 index 00000000..df8273ba --- /dev/null +++ b/Docs/IAMReX_documentation/source/references.rst @@ -0,0 +1,7 @@ +********** +References +********** + +.. bibliography:: refs.bib + :style: unsrt + :all: \ No newline at end of file diff --git a/Docs/IAMReX_documentation/source/refs.bib b/Docs/IAMReX_documentation/source/refs.bib new file mode 100644 index 00000000..76327c49 --- /dev/null +++ b/Docs/IAMReX_documentation/source/refs.bib @@ -0,0 +1,1437 @@ +@article{uhlmann2005immersed, + title={An immersed boundary method with direct forcing for the simulation of particulate flows}, + author={Uhlmann, Markus}, + journal={Journal of Computational Physics}, + volume={209}, + number={2}, + pages={448--476}, + year={2005}, + publisher={Elsevier} +} + +@article{sussman2000coupled, + title={{A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows}}, + author={Sussman, Mark and Puckett, Elbridge Gerry}, + journal={Journal of Computational Physics}, + volume={162}, + number={2}, + pages={301--337}, + year={2000}, + publisher={Elsevier} +} + +@inproceedings{natarajan2019actuator, + title={Actuator-line simulations of wind turbines with block-structured adaptive mesh refinement}, + author={Natarajan, Mahesh and Sitaraman, Hariswaran and Ananthan, Shreyas and Alan Sprague, Michael}, + booktitle={APS Division of Fluid Dynamics Meeting Abstracts}, + pages={C09--008}, + year={2019} +} + +@article{zeng2022subcycling, + title={A subcycling/non-subcycling time advancement scheme-based DLM immersed boundary method framework for solving single and multiphase fluid--structure interaction problems on dynamically adaptive grids}, + author={Zeng, Yadong and Bhalla, Amneet Pal Singh and Shen, Lian}, + journal={Computers \& Fluids}, + volume={238}, + pages={105358}, + year={2022}, + publisher={Elsevier} +} + +@article{zeng2023consistent, + title={{A consistent adaptive level set framework for incompressible two-phase flows with high density ratios and high Reynolds numbers}}, + author={Zeng, Yadong and Liu, Han and Gao, Qiang and Almgren, Ann and Bhalla, Amneet Pal Singh and Shen, Lian}, + journal={Journal of Computational Physics}, + volume={478}, + pages={111971}, + year={2023}, + publisher={Elsevier} +} + +@phdthesis{zeng2022numerical, + title={Numerical Simulations of the Two-phase flow and Fluid-Structure Interaction Problems with Adaptive Mesh Refinement}, + author={Zeng, Yadong}, + year={2022}, + school={University of Minnesota} +} + +@article{zhang2021amrex, + title={AMReX: Block-structured adaptive mesh refinement for multiphysics applications}, + author={Zhang, Weiqun and Myers, Andrew and Gott, Kevin and Almgren, Ann and Bell, John}, + journal={The International Journal of High Performance Computing Applications}, + volume={35}, + number={6}, + pages={508--526}, + year={2021}, + publisher={SAGE Publications Sage UK: London, England} +} + +@inproceedings{zeng2021subcycling, + title={A subcycling/non-subcycling time advancement scheme-based sharp-interface immersed boundary method framework for solving fluid-structure interaction problems on dynamically adaptive grids}, + author={Zeng, Yadong and Bhalla, Amneet Pal and He, Sida and Shen, Lian}, + booktitle={APS Division of Fluid Dynamics Meeting Abstracts}, + pages={F26--004}, + year={2021} +} + +@article{song2016hydrodynamic, + title={Hydrodynamic forces and coefficients on flexible risers undergoing vortex-induced vibrations in uniform flow}, + author={Song, Leijian and Fu, Shixiao and Zeng, Yadong and Chen, Yifan}, + journal={Journal of Waterway, Port, Coastal, and Ocean Engineering}, + volume={142}, + number={4}, + pages={04016001}, + year={2016}, + publisher={American Society of Civil Engineers} +} + +@book{faltinsen1993sea, + title={Sea loads on ships and offshore structures}, + author={Faltinsen, Odd}, + Volume={1}, + year={1993}, + publisher={Cambridge university press} +} + +@article{kolahdouz2020immersed, + title={An immersed interface method for discrete surfaces}, + author={Kolahdouz, Ebrahim M and Bhalla, Amneet Pal Singh and Craven, Brent A and Griffith, Boyce E}, + journal={Journal of Computational Physics}, + volume={400}, + pages={108854}, + year={2020}, + publisher={Elsevier} +} + +@article{zhang2004airflow, + title={Airflow structures and nano-particle deposition in a human upper airway model}, + author={Zhang, Z and Kleinstreuer, C}, + journal={Journal of Computational Physics}, + volume={198}, + number={1}, + pages={178--210}, + year={2004}, + publisher={Elsevier} +} + +@article{zeng2022aparallel, + title={A parallel cell-centered adaptive level set framework for efficient simulation of two-phase flows with subcycling and non-subcycling}, + author={Zeng, Yadong and Xuan, Anqing and Blaschke, Johannes and Shen, Lian}, + journal={Journal of Computational Physics}, + volume={448}, + pages={110740}, + year={2022}, + publisher={Elsevier} +} + +@article{zhang2019amrex, + title={{AMReX: a framework for block-structured adaptive mesh refinement}}, + author={Zhang, Weiqun and Almgren, Ann and Beckner, Vince and Bell, John and Blaschke, Johannes and Chan, Cy and Day, Marcus and Friesen, Brian and Gott, Kevin and Graves, Daniel and others}, + journal={Journal of Open Source Software}, + volume={4}, + number={37}, + year={2019}, + publisher={Lawrence Berkeley National Lab.(LBNL), Berkeley, CA (United States)} +} + +@article{almgren1998conservative, + title={{A conservative adaptive projection method for the variable density incompressible Navier--Stokes equations}}, + author={Almgren, Ann S and Bell, John B and Colella, Phillip and Howell, Louis H and Welcome, Michael L}, + journal={Journal of Computational Physics}, + volume={142}, + number={1}, + pages={1--46}, + year={1998}, + publisher={Elsevier} +} + +@article{bhalla2013unified, + title={{A unified mathematical framework and an adaptive numerical method for fluid--structure interaction with rigid, deforming, and elastic bodies}}, + author={Bhalla, Amneet Pal Singh and Bale, Rahul and Griffith, Boyce E and Patankar, Neelesh A}, + journal={Journal of Computational Physics}, + volume={250}, + pages={446--476}, + year={2013}, + publisher={Elsevier} +} + +@article{popinet2003gerris, + title={{Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries}}, + author={Popinet, St{\'e}phane}, + journal={Journal of Computational Physics}, + volume={190}, + number={2}, + pages={572--600}, + year={2003}, + publisher={Elsevier} +} + +@article{popinet2009accurate, + title={{An accurate adaptive solver for surface-tension-driven interfacial flows}}, + author={Popinet, St{\'e}phane}, + journal={Journal of Computational Physics}, + volume={228}, + number={16}, + pages={5838--5866}, + year={2009}, + publisher={Elsevier} +} + +@article{martin2000cell, + title={{A cell-centered adaptive projection method for the incompressible Euler equations}}, + author={Martin, Daniel F and Colella, Phillip}, + journal={Journal of Computational Physics}, + volume={163}, + number={2}, + pages={271--312}, + year={2000}, + publisher={Elsevier} +} + +@article{martin2008cell, + title={{A cell-centered adaptive projection method for the incompressible Navier--Stokes equations in three dimensions}}, + author={Martin, Daniel F and Colella, Phillip and Graves, Daniel}, + journal={Journal of Computational Physics}, + volume={227}, + number={3}, + pages={1863--1886}, + year={2008}, + publisher={Elsevier} +} + +@inproceedings{balaras2009adaptive, + title={Adaptive mesh refinement strategies for immersed boundary methods}, + author={Balaras, Elias and Vanella, Marcos}, + booktitle={47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition}, + pages={162}, + year={2009} +} + +@article{yadong2020osm, + title={Modelling Wave Energy Converter (WEC) pointer absorbers using AMR techniques with both subcycling and non-subcycling}, + author={Zeng, Yadong}, + journal={Authorea Preprints}, + year={2022}, + publisher={Authorea} +} + +@article{berger1989local, + title={{Local adaptive mesh refinement for shock hydrodynamics}}, + author={Berger, Marsha J and Colella, Phillip}, + journal={Journal of Computational Physics}, + volume={82}, + number={1}, + pages={64--84}, + year={1989}, + publisher={Elsevier} +} + +@article{berger1984adaptive, + title={{Adaptive mesh refinement for hyperbolic partial differential equations}}, + author={Berger, Marsha J and Oliger, Joseph}, + journal={Journal of Computational Physics}, + volume={53}, + number={3}, + pages={484--512}, + year={1984}, + publisher={Elsevier} +} + +@article{chorin1967numerical, + title={{The numerical solution of the Navier-Stokes equations for an incompressible fluid}}, + author={Chorin, Alexandre Joel}, + journal={Bulletin of the American Mathematical Society}, + volume={73}, + number={6}, + pages={928--931}, + year={1967} +} + +@article{sussman1999adaptive, + title={{An adaptive level set approach for incompressible two-phase flows}}, + author={Sussman, Mark and Almgren, Ann S and Bell, John B and Colella, Phillip and Howell, Louis H and Welcome, Michael L}, + journal={Journal of Computational Physics}, + volume={148}, + number={1}, + pages={81--124}, + year={1999}, + publisher={Elsevier} +} + +@article{almgren1996numerical, + title={{A numerical method for the incompressible Navier--Stokes equations based on an approximate projection}}, + author={Almgren, Ann S and Bell, John B and Szymczak, William G}, + journal={SIAM Journal on Scientific Computing}, + volume={17}, + number={2}, + pages={358--369}, + year={1996}, + publisher={SIAM} +} + +@TECHREPORT{rider1995approximate, + author = {William J. Rider}, + title = {Approximate Projection Methods for Incompressible Flow: Implementation, Variants and Robustness}, + institution = {Los Alamos National Laboratory}, + number = {LA-UR-94-2000}, + type = {LANL Unclassified Report}, + year = {1995} +} + +@inproceedings{zeng2019unified, + title={{A unified AMR framework for multiphase flow and fluid-structure interaction problems with both non-subcycling and subcycling}}, + author={Zeng, Yadong and Shen, Lian}, + booktitle={APS Division of Fluid Dynamics Meeting Abstracts}, + pages={S19--001}, + year={2019} +} + +@article{zeng2022parallel, + title={{A parallel cell-centered adaptive level set framework for efficient simulation of two-phase flows with subcycling and non-subcycling}}, + author={Zeng, Yadong and Xuan, Anqing and Blaschke, Johannes and Shen, Lian}, + journal={Journal of Computational Physics}, + volume={448}, + pages={110740}, + year={2022}, + publisher={Elsevier} +} + +@article{nonaka2011three, + title={{A three-dimensional, unsplit godunov method for scalar conservation laws}}, + author={Nonaka, Andy and May, Sandra and Almgren, Ann S and Bell, John B}, + journal={SIAM Journal on Scientific Computing}, + volume={33}, + number={4}, + pages={2039--2062}, + year={2011}, + publisher={SIAM} +} + +@inproceedings{bell1991efficient, + title={{An efficient second-order projection method for viscous incompressible flow}}, + author={Bell, John and Howell, Louis and Colella, Phillip}, + booktitle={10th Computational Fluid Dynamics Conference}, + pages={1560}, + year={1991} +} + +@article{griffith2012immersed, + title={{Immersed boundary model of aortic heart valve dynamics with physiological driving and loading conditions}}, + author={Griffith, Boyce E}, + journal={International journal for numerical methods in biomedical engineering}, + volume={28}, + number={3}, + pages={317--345}, + year={2012}, + publisher={Wiley Online Library} +} + +@article{griffith2007adaptive, + title={{An adaptive, formally second order accurate version of the immersed boundary method}}, + author={Griffith, Boyce E and Hornung, Richard D and McQueen, David M and Peskin, Charles S}, + journal={Journal of Computational Physics}, + volume={223}, + number={1}, + pages={10--49}, + year={2007}, + publisher={Elsevier} +} + +@article{bhalla2013forced, + title={A forced damped oscillation framework for undulatory swimming provides new insights into how propulsion arises in active and passive swimming}, + author={Bhalla, Amneet Pal Singh and Griffith, Boyce E and Patankar, Neelesh A}, + journal={PLoS Computational Biology}, + volume={9}, + number={6}, + pages={e1003097}, + year={2013}, + publisher={Public Library of Science} +} + +@article{khedkar2021inertial, + title={{The inertial sea wave energy converter (ISWEC) technology: device-physics, multiphase modeling and simulations}}, + author={Khedkar, Kaustubh and Nangia, Nishant and Thirumalaisamy, Ramakrishnan and Bhalla, Amneet Pal Singh}, + journal={Ocean Engineering}, + volume={229}, + pages={108879}, + year={2021}, + publisher={Elsevier} +} + +@article{yu2013reynolds, + title={{Reynolds-Averaged Navier--Stokes simulation of the heave performance of a two-body floating-point absorber wave energy system}}, + author={Yu, Yi-Hsiang and Li, Ye}, + journal={Computers \& Fluids}, + volume={73}, + pages={104--114}, + year={2013}, + publisher={Elsevier} +} + +@article{sharma2024exawind, + title={ExaWind: Open-source CFD for hybrid-RANS/LES geometry-resolved wind turbine simulations in atmospheric flows}, + author={Sharma, Ashesh and Brazell, Michael J and Vijayakumar, Ganesh and Ananthan, Shreyas and Cheung, Lawrence and deVelder, Nathaniel and Henry de Frahan, Marc T and Matula, Neil and Mullowney, Paul and Rood, Jon and others}, + journal={Wind Energy}, + volume={27}, + number={3}, + pages={225--257}, + year={2024}, + publisher={Wiley Online Library} +} + +@inproceedings{mullowney2021preparing, + title={Preparing an incompressible-flow fluid dynamics code for exascale-class wind energy simulations}, + author={Mullowney, Paul and Li, Ruipeng and Thomas, Stephen and Ananthan, Shreyas and Sharma, Ashesh and Rood, Jon S and Williams, Alan B and Sprague, Michael A}, + booktitle={Proceedings of the international conference for high performance computing, networking, storage and analysis}, + pages={1--16}, + year={2021} +} + +@article{fujimoto2006electromagnetic, + title={{Electromagnetic full particle code with adaptive mesh refinement technique: Application to the current sheet evolution}}, + author={Fujimoto, Keizo and Machida, Shinobu}, + journal={Journal of Computational Physics}, + volume={214}, + number={2}, + pages={550--566}, + year={2006}, + publisher={Elsevier} +} + +@article{balsara2001divergence, + title={{Divergence-free adaptive mesh refinement for magnetohydrodynamics}}, + author={Balsara, Dinshaw S}, + journal={Journal of Computational Physics}, + volume={174}, + number={2}, + pages={614--648}, + year={2001}, + publisher={Elsevier} +} + +@article{santilli2015stratified, + title={{The stratified ocean model with adaptive refinement (SOMAR)}}, + author={Santilli, Edward and Scotti, Alberto}, + journal={Journal of Computational Physics}, + volume={291}, + pages={60--81}, + year={2015}, + publisher={Elsevier} +} + +@article{mirzadeh2016parallel, + title={{Parallel level-set methods on adaptive tree-based grids}}, + author={Mirzadeh, Mohammad and Guittet, Arthur and Burstedde, Carsten and Gibou, Frederic}, + journal={Journal of Computational Physics}, + volume={322}, + pages={345--364}, + year={2016}, + publisher={Elsevier} +} + +@article{peraire1987adaptive, + title={{Adaptive remeshing for compressible flow computations}}, + author={Peraire, Jaime and Vahdati, Morgan and Morgan, Ken and Zienkiewicz, Olgierd C}, + journal={Journal of Computational Physics}, + volume={72}, + number={2}, + pages={449--466}, + year={1987}, + publisher={Elsevier} +} + +@article{popinet2007tree, + title={{A tree-based solver for adaptive ocean modelling}}, + author={Popinet, St{\'e}phane and Rickard, Graham}, + journal={Ocean Modelling}, + volume={16}, + number={3-4}, + pages={224--249}, + year={2007}, + publisher={Elsevier} +} + +@article{van2018towards, + title={{Towards adaptive grids for atmospheric boundary-layer simulations}}, + author={van Hooft, J Antoon and Popinet, St{\'e}phane and van Heerwaarden, Chiel C and van der Linden, Steven JA and de Roode, Stephan R and van de Wiel, Bas JH}, + journal={Boundary-Layer Meteorology}, + volume={167}, + number={3}, + pages={421--443}, + year={2018}, + publisher={Springer} +} + +@inproceedings{williamschen2013parallel, + title={{Parallel anisotropic block-based adaptive mesh refinement algorithm for three-dimensional flows}}, + author={Williamschen, Michael and Groth, Clinton P}, + booktitle={21st AIAA Computational Fluid Dynamics Conference}, + pages={2442}, + year={2013} +} + +@article{sverdrup2018highly, + title={Highly parallelisable simulations of time-dependent viscoplastic fluid flow with structured adaptive mesh refinement}, + author={Sverdrup, Knut and Nikiforakis, Nikolaos and Almgren, Ann}, + journal={Physics of Fluids}, + volume={30}, + number={9}, + pages={093102}, + year={2018}, + publisher={AIP Publishing LLC} +} + +@article{peskin2002immersed, + title={{The immersed boundary method}}, + author={Peskin, Charles S}, + journal={Acta Numerica}, + volume={11}, + pages={479--517}, + year={2002}, + publisher={{Cambridge University Press}} +} + +@article{nangia2019dlm, + title={{A DLM immersed boundary method based wave-structure interaction solver for high density ratio multiphase flows}}, + author={Nangia, Nishant and Patankar, Neelesh A and Bhalla, Amneet Pal Singh}, + journal={Journal of Computational Physics}, + volume={398}, + pages={108804}, + year={2019}, + publisher={Elsevier} +} + +@article{kempe2012improved, + title={{An improved immersed boundary method with direct forcing for the simulation of particle laden flows}}, + author={Kempe, Tobias and Fr{\"o}hlich, Jochen}, + journal={Journal of Computational Physics}, + volume={231}, + number={9}, + pages={3663--3684}, + year={2012}, + publisher={Elsevier} +} + +@article{kempe2012collision, + title={{Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids}}, + author={Kempe, Tobias and Fr{\"o}hlich, Jochen}, + journal={Journal of Fluid Mechanics}, + volume={709}, + pages={445--489}, + year={2012}, + publisher={Cambridge University Press} +} + +@article{breugem2012second, + title={{A second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows}}, + author={Breugem, Wim-Paul}, + journal={Journal of Computational Physics}, + volume={231}, + number={13}, + pages={4469--4498}, + year={2012}, + publisher={Elsevier} +} + +@article{gong2023cp3d, + title={{CP3d: A comprehensive Euler-Lagrange solver for direct numerical simulation of particle-laden flows}}, + author={Gong, Zheng and Wu, Zi and An, Chenge and Zhang, Bangwen and Fu, Xudong}, + journal={Computer Physics Communications}, + volume={286}, + pages={108666}, + year={2023}, + publisher={Elsevier} +} + +@article{akiki2016immersed, + title={{Immersed boundary method with non-uniform distribution of Lagrangian markers for a non-uniform Eulerian mesh}}, + author={Akiki, Georges and Balachandar, S}, + journal={Journal of Computational Physics}, + volume={307}, + pages={34--59}, + year={2016}, + publisher={Elsevier} +} + +@article{zhu2022particle, + title={{Particle resolved simulation of sediment transport by a hybrid parallel approach}}, + author={Zhu, Zhengping and Hu, Ruifeng and Lei, Yinghaonan and Shen, Lian and Zheng, Xiaojing}, + journal={International Journal of Multiphase Flow}, + volume={152}, + pages={104072}, + year={2022}, + publisher={Elsevier} +} + +@article{zhu2023multiple, + title={{A multiple-time-step integration algorithm for particle-resolved simulation with physical collision time}}, + author={Zhu, Zhengping and Hu, Ruifeng and Zheng, Xiaojing}, + journal={International Journal of Multiphase Flow}, + volume={163}, + pages={104411}, + year={2023}, + publisher={Elsevier} +} + +@article{wang2023drag, + title={{Drag model of finite-sized particle in turbulent wall-bound flow over sediment bed}}, + author={Wang, Ping and Lei, Yinghaonan and Zhu, Zhengping and Zheng, Xiaojing}, + journal={Journal of Fluid Mechanics}, + volume={964}, + pages={A9}, + year={2023}, + publisher={Cambridge University Press} +} + +@article{cui2018sharp, + title={A sharp-interface immersed boundary method for simulating incompressible flows with arbitrarily deforming smooth boundaries}, + author={Cui, Zuo and Yang, Zixuan and Jiang, Hong-Zhou and Huang, Wei-Xi and Shen, Lian}, + journal={International Journal of Computational Methods}, + volume={15}, + number={01}, + pages={1750080}, + year={2018}, + 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+ year={2023}, + publisher={Elsevier} +} + +@article{liu2023experimental, + title={Experimental and fluid flow simulation studies of laser-electrochemical hybrid manufacturing of micro--nano symbiotic superamphiphobic surfaces}, + author={Liu, Yang and Liu, Xinyu and Zhang, Zhaoyang and Lu, Jinzhong and Wang, Yufeng and Xu, Kun and Zhu, Hao and Wang, Bo and Lin, Liqu and Xue, Wei}, + journal={The Journal of Chemical Physics}, + volume={159}, + number={11}, + year={2023}, + publisher={AIP Publishing} +} + +@article{yang2024boundary, + title={Boundary fluid constraints during electrochemical jet machining of large size emerging titanium alloy aerospace parts in gas--liquid flows: Experimental and numerical simulation}, + author={Yang, LIU and Ningsong, QU and Hansong, LI and ZHANG, Zhaoyang}, + journal={Chinese Journal of Aeronautics}, + year={2024}, + publisher={Elsevier} +} + +@article{pozzetti2019parallel, + title={{A parallel dual-grid multiscale approach to CFD--DEM couplings}}, + author={Pozzetti, Gabriele and Jasak, Hrvoje and Besseron, Xavier and Rousset, Alban and Peters, Bernhard}, + journal={Journal of computational physics}, + volume={378}, + pages={708--722}, + year={2019}, + publisher={Elsevier} +} + +@article{myers2021porting, + title={{Porting WarpX to GPU-accelerated platforms}}, + author={Myers, Andrew and Almgren, A and Amorim, Ligia Diana and Bell, J and Fedeli, Luca and Ge, Lixin and Gott, Kevin and Grote, David P and Hogan, M and Huebl, Axel and others}, + journal={Parallel Computing}, + volume={108}, + pages={102833}, + year={2021}, + publisher={Elsevier} +} + +@article{yousefi2023role, + title={On the role of inertia in channel flows of finite-size neutrally buoyant particles}, + author={Yousefi, Ali and Costa, Pedro and Picano, Francesco and Brandt, Luca}, + journal={Journal of Fluid Mechanics}, + volume={955}, + pages={A30}, + year={2023}, + publisher={Cambridge University Press} +} + +@article{xia2020effects, + title={Effects of the collision model in interface-resolved simulations of particle-laden turbulent channel flows}, + author={Xia, Yan and Xiong, Hongbing and Yu, Zhaosheng and Zhu, Chenlin}, + journal={Physics of Fluids}, + volume={32}, + number={10}, + year={2020}, + publisher={AIP Publishing} +} + +@article{fan2023three, + title={A three-dimensional fictitious domain method for direct numerical simulations of particle-laden flows with heat transfer}, + author={Fan, Peifei and Lin, Zhaowu and Xu, Jian and Yu, Zhaosheng}, + journal={Physics of Fluids}, + volume={35}, + number={6}, + year={2023}, + publisher={AIP Publishing} +} + +@article{sharma2022coupled, + title={A coupled distributed Lagrange multiplier (DLM) and discrete element method (DEM) approach to simulate particulate flow with collisions}, + author={Sharma, Govind and Nangia, Nishant and Bhalla, Amneet Pal Singh and Ray, Bahni}, + journal={Powder Technology}, + volume={398}, + pages={117091}, + year={2022}, + publisher={Elsevier} +} + +@article{tschisgale2018general, + title={A general implicit direct forcing immersed boundary method for rigid particles}, + author={Tschisgale, Silvio and Kempe, Tobias and Fr{\"o}hlich, Jochen}, + journal={Computers \& Fluids}, + volume={170}, + pages={285--298}, + year={2018}, + publisher={Elsevier} +} + +@article{wang2017simple, + title={A simple and efficient implicit direct forcing immersed boundary model for simulations of complex flow}, + author={Wang, Wen-Quan and Yan, Yan and Tian, Fang-Bao}, + journal={Applied Mathematical Modelling}, + volume={43}, + pages={287--305}, + year={2017}, + publisher={Elsevier} +} \ No newline at end of file

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zQP71e0t5VPYzYh}VvijyEiJ7alCVLHXv8#G2ex3p*bN#(el_n(zINFG2gay)YIGBX zpCm_}VN;`_. + +For example, if we want to compile in the ``FlowPastSphere``, refer to the following steps: + +#. cd to the FlowPastSphere directory + + .. code:: shell + + cd IAMReX/Tutorials/FlowPastSphere + +#. Modify compilation parameters in GNUmakefile. + + The compilation parameters depend on your computing platform. If you use MPI to run your program, then set USE_MPI = TRUE. If you are running the program with Nvidia GPU(CUDA), then set USE_CUDA = TRUE. When using GPU runtime, please make sure your CUDA environment is ok. + +#. Compile + + With the above settings, you can compile the program: + + .. code:: shell + + make + + You can add parameters after make, such as -f your_make_file to customize your parameter file, and -j 8 to specify 8 threads to participate in the compilation. + +If the compilation is successful, an executable file will be generated. Usually the executable file is named in the following format:amr[DIM].[Compiler manufacturers].[computing platform].[is Debug].ex. The executable file name of the Release version of the three-dimensional compiled using the GNU compiler in the MPI environment is: amr3d.GNU.MPI.ex. + + +Running the code +---------------- +You should takes an input file as its first command-line argument. The file may contain a set of parameter definitions that will overrides defaults set in the code. In the ``FlowPastSphere``, you can find a file named ``inputs.3d.flow_past_sphere``, run: + + .. code:: shell + + ./amr3d.GNU.MPI.ex inputs.3d.flow_past_sphere + +If you use ``MPI`` to run your program, you can type: + + .. code:: shell + + mpirun -np how_many_threads amr3d.GNU.MPI.ex inputs.3d.flow_past_sphere + +This code typically generates subfolders in the current folder that are named ``plt00000``, ``plt00010``, etc, and ``chk00000``, ``chk00010``, etc. These are called plotfiles and checkpoint files. The plotfiles are used for visualization of derived fields; the checkpoint files are used for restarting the code. + + +Key parameters +--------------- + +.. tip:: + you can find more parameters in `IAMR guide `_. + +.. list-table:: NavierStokes parameters + :widths: 40 100 20 20 + :header-rows: 1 + + * - + - Description + - Type + - Default + * - do_diffused_ib + - enable IBM + - Int + - 0 + * - fluid_rho + - density of fluid + - Real + - 1.0 + +The above parameters are designed for the immersed boundary (IB) method. Additionally, the ``particle.input`` flag (such as ``particle_inputs``) must be specified to define IB-related parameters. The program will query these parameters through this flag. The specific parameters include the following: + +.. list-table:: DiffusedIB parameters + :widths: 40 100 20 20 + :header-rows: 1 + + * - + - Description + - Type + - Default + * - x + - particle x position + - Real Array + - 0.0 + * - y + - particle y position + - Real Array + - 0.0 + * - z + - particle z position + - Real Array + - 0.0 + * - rho + - density of particles + - Real Array + - 1.0 + * - radius + - radius of particles + - Real Array + - 0.0 + * - velocity_x + - The initial velocity of the particles in the x direction + - Real Array + - 0.0 + * - velocity_y + - The initial velocity of the particles in the y direction + - Real Array + - 0.0 + * - velocity_z + - The initial velocity of the particles in the z direction + - Real Array + - 0.0 + * - omega_x + - The initial angular velocity of the particle around the x-axis + - Real Array + - 0.0 + * - omega_y + - The initial angular velocity of the particle around the y-axis + - Real Array + - 0.0 + * - omega_z + - The initial angular velocity of the particle around the z-axis + - Real Array + - 0.0 + * - TLX + - Particle freedom in x-direction + - Int Array + - 0 + * - TLY + - Particle freedom in y-direction + - Int Array + - 0 + * - TLZ + - Particle freedom in z-direction + - Int Array + - 0 + * - RLX + - Particle rotation about x-axis + - Int Array + - 0 + * - RLY + - Particle rotation about y-axis + - Int Array + - 0 + * - RLZ + - Particle rotation about z-axis + - Int Array + - 0 + * - RD + - particle retraction distance + - Real + - 0.0 + * - write_freq + - How many steps to export the particle information + - Int + - 1 + * - LOOP_NS + - Ns loop time + - Int + - 2 + * - LOOP_SOLID + - particle update steps + - Int + - 1 + * - start_step + - How much steps does it take for the particles to move + - Int + - -1 + * - collision_model + - particle collision model + - Int + - 1.0 + * - verbose + - Whether to output debug information + - Int + - 0 + * - init + - particle init file path + - file path + - + +Among the above parameters, array-type parameters are used to specify parameters for multiple particles individually, or define particle positions via an init file (e.g., a precomputed position data file). +If particle positions are provided through an external file, other array-type parameters only need to provide a single value, which will be applied to all particles uniformly. + +example inputs file as blow : + +:: + + #******************************************************************************* + # INPUTS.3D.FLOW_PAST_SPHERE + #******************************************************************************* + + #NOTE: You may set *either* max_step or stop_time, or you may set them both. + + # Maximum number of coarse grid timesteps to be taken, if stop_time is + # not reached first. + max_step = 2 + + # Time at which calculation stops, if max_step is not reached first. + stop_time = 100.0 + + ns.fixed_dt = 0.01 + ns.cfl = 0.3 + ns.init_iter = 0 + + # Diffused IB input file + particle.input = particle_inputs + + # Refinement criterion, use vorticity and presence of tracer + amr.refinement_indicators = tracer + + amr.max_level = 0 # maximum number of levels of refinement + # amr.tracer.value_greater = 0.1 + # amr.tracer.value_less = 1.1 + amr.tracer.field_name = tracer + amr.tracer.in_box_lo = 0.5 0.5 0.5 + amr.tracer.in_box_hi = 1.5 1.5 1.5 + + amr.blocking_factor = 8 + + #******************************************************************************* + + # Number of cells in each coordinate direction at the coarsest level + # amr.n_cell = 16 8 8 + amr.n_cell = 256 128 128 + # amr.n_cell = 288 128 128 + amr.max_grid_size = 16 + # amr.max_grid_size = 32 + + #******************************************************************************* + + # Interval (in number of level l timesteps) between regridding + amr.regrid_int = 1 # regrid_int + + #******************************************************************************* + + # Refinement ratio as a function of level + amr.ref_ratio = 2 2 2 2 + + #******************************************************************************* + + # Sets the "NavierStokes" code to be verbose + ns.v = 1 + nodal_proj.verbose = 1 + mac_proj.verbose = 1 + + # mac_proj.mac_tol = 0.1 + # mac_proj.mac_abs_tol = 0.1 + + #******************************************************************************* + + # Sets the "amr" code to be verbose + amr.v = 1 + + #******************************************************************************* + + # Interval (in number of coarse timesteps) between checkpoint(restart) files + + amr.check_int = 4000 + + #amr.restart = chk01400 + + #******************************************************************************* + + # Interval (in number of coarse timesteps) between plot files + amr.plot_int = 1 + + + #******************************************************************************* + + # Viscosity coefficient + ns.vel_visc_coef = 0.01 + + #******************************************************************************* + + # Diffusion coefficient for first scalar + ns.scal_diff_coefs = 0.0 + + #******************************************************************************* + + # Forcing term defaults to rho * abs(gravity) "down" + ns.gravity = 0.0 # -9.8 + + #******************************************************************************* + + # skip level_projector + ns.skip_level_projector = 0 + + #******************************************************************************* + + # subcycling vs. non-subcycling + amr.subcycling_mode = None + + #******************************************************************************* + + # Set to 0 if x-y coordinate system, set to 1 if r-z. + geometry.coord_sys = 0 + + #******************************************************************************* + + # Physical dimensions of the low end of the domain. + geometry.prob_lo = 0. 0. 0. + + # Physical dimensions of the high end of the domain. + geometry.prob_hi = 20. 10. 10. + + #******************************************************************************* + + #Set to 1 if periodic in that direction + geometry.is_periodic = 0 1 1 + + #******************************************************************************* + + # Boundary conditions on the low end of the domain. + ns.lo_bc = 1 0 0 + + # Boundary conditions on the high end of the domain. + ns.hi_bc = 2 0 0 + + # 0 = Interior/Periodic 3 = Symmetry + # 1 = Inflow 4 = SlipWall + # 2 = Outflow 5 = NoSlipWall + + # Boundary condition + xlo.velocity = 1. 0. 0. + + #******************************************************************************* + + # Problem parameters + prob.probtype = 1 + + #******************************************************************************* + + # Add vorticity to the variables in the plot files. + # amr.derive_plot_vars = avg_pressure + + #******************************************************************************* + ns.isolver = 1 + ns.do_diffused_ib = 1 + ns.fluid_rho = 1.0 + + #ns.sum_interval = 1 + + particles.do_nspc_particles = 0 + + nodal_proj.proj_tol = 1.e-8 + nodal_proj.proj_abs_tol = 1.e-9 + + nodal_proj.maxiter = 200 + nodal_proj.bottom_maxiter = 200 + + mac_proj.mac_tol = 1.e-8 + mac_proj.mac_abs_tol = 1.e-9 + + + ############################ + # # + # Diffused IB cfg file # + # # + ############################ + + # particle's location + # x = p1x p2x p3x ... + particle_inputs.x = 5.0 + particle_inputs.y = 5.0 + particle_inputs.z = 5.0 + + # particle's density + # rho = p1r p2r p3r ... + particle_inputs.rho = 1.0 + + # particle's radius + # single + particle_inputs.radius = 0.5 + + # particle's velocity + # vx = p1vx p2vx p3vx ... + particle_inputs.velocity_x = 0.0 + particle_inputs.velocity_y = 0.0 + particle_inputs.velocity_z = 0.0 + + # particle's omega + # omega = p1omega_x p2omega_x p3omega_x ... + particle_inputs.omega_x = 0.0 + particle_inputs.omega_y = 0.0 + particle_inputs.omega_z = 0.0 + + # particle's 6DOF + # TLX = p1tl p2tl ... + particle_inputs.TLX = 0 + particle_inputs.TLY = 0 + particle_inputs.TLZ = 0 + particle_inputs.RLX = 0 + particle_inputs.RLY = 0 + particle_inputs.RLZ = 0 + + + # msg print + particle_inputs.verbose = 1 + +If you want to know more about the parameters, you can check the `AMReX `_. \ No newline at end of file diff --git a/Docs/IAMReX_documentation/source/Introduction_Chapter.rst b/Docs/IAMReX_documentation/source/Introduction_Chapter.rst new file mode 100644 index 00000000..7e1684c7 --- /dev/null +++ b/Docs/IAMReX_documentation/source/Introduction_Chapter.rst @@ -0,0 +1,46 @@ +Introduction +=================== + +This IAMReX repo extends the capability of original `IAMR `_ codes, aiming at simulating the multiphase incompressible flows and fluid structure interaction problems on both CPUs and GPUs with/without subcycling. The Navier-Stokes euqations are solved on an adaptive semi-staggered grid using the projection method. The gas-liquid interface is captured using the level set (LS) method. The fluid-solid interface is resolved using the multidirect forcing immersed boundary method (IBM). The particle-wall as well as the particle-particle collisions are also captured by the adaptive collision time model (ACTM). + + +Features +------------------ + +Key software and algorithmic features of IAMR include: + +* LS method and reinitialization schemes + +* Multidirect forcing Immersed Boundary Method + +* Particle Collision Algorithms with Discrete Element Method + +Figures +------------------ + +.. figure:: ./GettingStarted/RSV.jpeg + :align: center + :alt: Profiles of drop interface in the RSV problem at t/T=1 after one rotation. Black line: Analytical Solution; Red line: 64*64; Blue line: 128*128; Green line: 256*256 + :width: 5.00000in + + Profiles of drop interface in the RSV problem at t/T=1 after one rotation. Black line: Analytical Solution; Red line: 64*64; Blue line: 128*128; Green line: 256*256 + +.. figure:: ./GettingStarted/IAMR_LSAMR.png + :align: center + :alt: (a) Density profile at t/T=2.42 using LS method. (b) Density profile at t/T=2.42 using IAMR convective scheme. + :width: 5.00000in + + Density profile: a. Density profile at t/T=2.42 using LS method. b. Density profile at t/T=2.42 using IAMR convective scheme. + +.. figure:: ./GettingStarted/RT_tip.png + :align: center + :alt: Comparison of the tip locations of the falling fluid and the rising fluid. + :width: 5.00000in + + Comparison of the tip locations of the falling fluid and the rising fluid. + +.. figure:: ./GettingStarted/Monodisperse.png + :align: center + :width: 5.00000in + + Contours of velocity magnitude in yz plane diff --git a/Docs/IAMReX_documentation/source/Results.rst b/Docs/IAMReX_documentation/source/Results.rst new file mode 100644 index 00000000..b6dde6b4 --- /dev/null +++ b/Docs/IAMReX_documentation/source/Results.rst @@ -0,0 +1,80 @@ +.. _Chap:Results: + +Validation Cases +================ + +Flow Past Fixed Sphere +---------------------- + +.. Figure:: ./Results/FlowPastSphere.png + :align: center + :width: 5.0in + + The schematic of the flow passing through the spherical particles + +we validate the accuracy and efficacy of our adaptive solver by simulating a spherical particle in uniform flow with different particle Reynolds numbers. The diameter of the particle is :math:`D_p = 1`, the computational domain is :math:`L_x \times L_y \times L_z = 20D_p \times 10D_p \times 10D_p`, the distance of the particle from the inlet is :math:`d = 5D_p` and located in the center of the yz plane. The inlet and outlet boundaries are applied in the x direction and the inlet velocity :math:`U` is :math:`1m/s`. Both y and z directions are periodic boundaries. + +The influence of AMR on the simulation results is investigated by using the subcycling method with different levels. As shown in Fig. + +.. Figure:: ./Results/FlowPastSphereResult.png + :align: center + :width: 5.0in + + The drag coefficient of the particle under uniform flows varies with Particle Reynolds number at different AMR levels. + +Three different types of grid were selected: level 0 indicates the single-level grid containing no AMR, level 1 indicates the two-level grid, and level 2 indicates the three-level grid. For all three types of grid, the ratio of the diameter of the particles to the grid spacing on the finest level is 16. The drag force, including the contributions of Lagrangian force and the PVF function, is calculated by + +.. math:: + \mathbf{F}_D=-\rho_f \sum_{l=1}^{N_L} \mathbf{F}_l^{n+1/2} \Delta V_l+\rho_f \frac{d}{d t}\left(\int_{V_p} \mathbf{u} d V\right), + +The theoretical S-N law for calculating the drag coefficient of the shaped particles is + +.. math:: + C_D = (24/Re_p)(1+0.15Re_p^{0.687}), + +which is proposed by schiller etal, and :math:`Re_p = UD_p/\nu` represents the particle Reynolds number. It can be seen from above Fig that the present results under different particle Reynolds numbers are in good agreement with S-N law. The fact that different levels of grid produce the nearly identical results validated the accuracy of our solver on the adaptive grid. + + +Cluster of monodisperse particles +--------------------------------- + +We demonstrate the accuracy and efficacy of our codes for simulating clusters of particles on the multi-level grid. As shown in Fig + +.. figure:: ./Results/MonodisperseParticlesAMR.png + :align: center + :width: 7.0in + + Monodisperse particles on a three-level AMR grid + +80 particles of diameter :math:`D = 1` are randomly distributed in a channel of size :math:`L_x\times L_y \times L_z = 10\times 20 \times 10`. To choose an optimal interaction number :math:`N_s` in this complex configuration, the maximum error of the no-slip boundary condition among 80 particles is tested with a unit flow field :math:`u=(1,0,0)`.the maximum error of no-slip condition decreases as :math:`N_s` increases and it is strongly reduced for :math:`N_s=2`. According to the selection suggestions provided by Breugem etal, :math:`N_s=2` is the optimal value for balancing the accuracy of the no-slip boundary and the computational efficiency. After determining :math:`N_s`, the fluid flow is driven by applying a pressure gradient of 1.0 in the z direction. This case can represent a porous medium with a volume fraction of 0.02. Three levels of the AMR grid is applied. The grid resolution on the finest level is :math:`d/h=16`. Since the multi-direct forcing immersed boundary method and fictitious domain method require cube grid cells, the grid cell requirement is equals to case 1 in Table. + + +------+---------+---------+---------+-------------+ + | case | level 0 | level 1 | level 2 | Total cells | + +======+=========+=========+=========+=============+ + | 1 | 8192000 | | | 8192000 | + +------+---------+---------+---------+-------------+ + | 2 | 128000 | 534656 | 1593664 | 2256320 | + +------+---------+---------+---------+-------------+ + +Compared with them, our algorithm has a 72.5% grid reduction with :math:`d/h=16`. And it has a 62.5% Lagrangian markers reduction compared with the DLM method with :math:`d/h=16`. + +When the simulation reaches the steady state, the total pressure drop balances the IB force generated by all particles in the streamwise z direction. Following the equation in akiki etal, the theoretical drag force is given by + +.. math:: + F_{theory} = (\frac{\Delta p}{\Delta z}L_z)L_xL_y + +Fig represents the velocity contour of three different interfaces in the x direction at the steady state. + +.. figure:: ./Results/MonodispersSliceResult.png + :align: center + :width: 5.0in + + Contours of velocity magnitude in :math:`yz` plane at the different x position: (a) x=2.5; (b) x=5.0; (c) x=7.5 + +The flow passes around the particles and generates the wakes behind. Fig. shows the time series of total IB force for all particles. The resistance gradually reaches a steady state after 40000 steps. In this case, the theoretical value of drag force given by :math:`F_{theory}` is 2000, while the present average values at steady state with :math:`N_s=2` and 4 are all converged around 2000. It indicates that :math:`N_s=2` is sufficient for this case. 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