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Support analytically defining patch variables in all case files
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‎.gitignore‎

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*.nsys-rep
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*.sqlite
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docs/*/initial*
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docs/*/result*
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docs/documentation/examples.md
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examples/*batch/*/
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examples/*/D/*
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examples/*/p*
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examples/*/fort.1
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examples/*/*.sh
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examples/*/*.err
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examples/*/viz/
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examples/*.jpg
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examples/*.png
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*.mod

‎CMakeLists.txt‎

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@@ -414,6 +414,8 @@ if (MFC_DOCUMENTATION)
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set(DOXYGEN_HTML_OUTPUT "\"${CMAKE_CURRENT_BINARY_DIR}/${target}\"")
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set(DOXYGEN_MATHJAX_CODEFILE "\"${CMAKE_CURRENT_SOURCE_DIR}/docs/config.js\"")
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set(DOXYGEN_PROJECT_LOGO "\"${CMAKE_CURRENT_SOURCE_DIR}/docs/res/icon.ico\"")
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set(DOXYGEN_IMAGE_PATH "\"${CMAKE_CURRENT_SOURCE_DIR}/docs/res\"\
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\"${CMAKE_CURRENT_SOURCE_DIR}/docs/${target}\"")
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file(MAKE_DIRECTORY "${DOXYGEN_OUTPUT_DIRECTORY}")
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OUTPUT "${CMAKE_CURRENT_BINARY_DIR}/${target}/html/index.html"
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DEPENDS "${CMAKE_CURRENT_BINARY_DIR}/${target}-Doxyfile"
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"${${target}_SRCs}"
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COMMAND "${DOXYGEN_EXECUTABLE}"
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"${target}-Doxyfile"
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COMMAND "bash" "${CMAKE_CURRENT_SOURCE_DIR}/docs/examples.sh"
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"${CMAKE_CURRENT_SOURCE_DIR}" &&
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"${DOXYGEN_EXECUTABLE}" "${target}-Doxyfile"
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WORKING_DIRECTORY "${CMAKE_CURRENT_BINARY_DIR}"
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COMMENT "${target}: Generating documentation"
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)

‎docs/Doxyfile.in‎

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# that contain images that are to be included in the documentation (see the
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# \image command).
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IMAGE_PATH = ../res
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IMAGE_PATH = @DOXYGEN_IMAGE_PATH@
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# The INPUT_FILTER tag can be used to specify a program that doxygen should
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# invoke to filter for each input file. Doxygen will invoke the filter program

‎docs/documentation/case.md‎

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@@ -139,27 +139,66 @@ the grid stretching funciton is applied and has a default value of one.
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### 3. Patches
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| Parameter | Type | Description |
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| ---: | :----: | :--- |
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| `num_patches` | Integer | Number of initial condition geometric patches. |
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| `num_fluids` | Integer | Number of fluids/components present in the flow. |
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| `geometry` * | Integer | Geometry configuration of the patch. |
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| `alter_patch(i)` * | Logical | Alter the $i$-th patch. |
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| `x[y,z]_centroid` * | Real | Centroid of the applied geometry in the $[x,y,z]$-direction. |
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| `length_x[y,z]` * | Real | Length, if applicable, in the $[x,y,z]$-direction. |
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| `radius` * | Real | Radius, if applicable, of the applied geometry. |
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| `smoothen` * | Logical | Smoothen the applied patch. |
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| `smooth_patch_id` * | Integer | A patch with which the applied patch is smoothened. |
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| `smooth_coeff` * | Real | Smoothen coefficient. |
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| `alpha(i)` * | Real | Volume fraction of fluid $i$. |
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| `alpha_rho(i)` * | Real | Partial density of fluid $i$. |
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| `pres` * | Real | Pressure. |
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| `vel(i)` * | Real | Velocity in direction $i$. |
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| Parameter | Type | Analytical Definition | Description |
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| ---: | :----: | :----: | :--- |
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| `num_patches` | Integer | Not Supported | Number of initial condition geometric patches. |
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| `num_fluids` | Integer | Not Supported | Number of fluids/components present in the flow. |
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| `geometry` * | Integer | Not Supported | Geometry configuration of the patch. |
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| `alter_patch(i)` * | Logical | Not Supported | Alter the $i$-th patch. |
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| `x[y,z]_centroid` * | Real | Not Supported | Centroid of the applied geometry in the $[x,y,z]$-direction. |
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| `length_x[y,z]` * | Real | Not Supported | Length, if applicable, in the $[x,y,z]$-direction. |
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| `radius` * | Real | Not Supported | Radius, if applicable, of the applied geometry. |
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| `smoothen` * | Logical | Not Supported | Smoothen the applied patch. |
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| `smooth_patch_id` * | Integer | Not Supported | A patch with which the applied patch is smoothened. |
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| `smooth_coeff` * | Real | Not Supported | Smoothen coefficient. |
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| `alpha(i)` * | Real | Supported | Volume fraction of fluid $i$. |
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| `alpha_rho(i)` * | Real | Supported | Partial density of fluid $i$. |
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| `pres` * | Real | Supported | Pressure. |
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| `vel(i)` * | Real | Supported | Velocity in direction $i$. |
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*: These parameters should be prepended with `patch_icpp(j)%` where $j$ is the patch index.
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The Table lists the patch parameters. The parameters define the geometries and physical parameters of fluid components (patch) in the domain at initial condition. Note that the domain must be fully filled with patche(s). The code outputs error messages when an empty region is left in the domain.
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#### Analytical Definition of Primitive Variables
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Some parameters, as described above, can be defined by analytical functions in the input file. For example, one can define the following patch:
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```json
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'patch_icpp(2)%geometry' : 15,
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'patch_icpp(2)%x_centroid' : 0.25,
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'patch_icpp(2)%length_x' : 9.5,
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'patch_icpp(2)%vel(1)' : 0.,
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'patch_icpp(2)%pres' : 1.,
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'patch_icpp(2)%alpha_rho(1)': '1 + 0.1*sin(20*x*pi)',
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'patch_icpp(2)%alpha(1)' : 1.,
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```
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where `alpha_rho` is defined with the `1 + 0.1*sin(20*x*pi)` function.
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The expressions are interpreted as Fortran code, in the execution context and scope of the function that defines the patch.
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Additionally, the following variables are made available as shorthand:
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| Shorthand | Expands To | Shorthand | Expands To | Shorthand | Expands To |
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| --------- | ------------------------ | --------- | ------------------------- | --------- | ------------------------ |
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| `x` | `x_cc(i)` | `lx` | The patch's `length_x` | `xc` | The patch's `x_centroid` |
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| `y` | `y_cc(j)` | `ly` | The patch's `length_y` | `yc` | The patch's `y_centroid` |
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| `z` | `z_cc(k)` | `lz` | The patch's `length_z` | `zc` | The patch's `z_centroid` |
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| `eps` | The patch's `epsilon` | `beta` | The patch's `beta` | `radii` | The patch's `radii` |
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| `tau_e` | The patch's `tau_e` | `r` | The patch's `radius` | `pi` and `e` | $\pi$ and $e$ |
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where $(i,j,k)$ are the grid-indices of the current cell in each coordinate direction.
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In the example above, the following code is generated:
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```f90
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if (patch_id == 2) then
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q_prim_vf(contxb)%sf(i, 0, 0) = 1 + 0.1*sin(20*x_cc(i)*3.141592653589793)
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end if
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```
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#### Parameter Descriptions
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- `num_patches` defines the total number of patches defined in the domain. The number has to be a positive integer.
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- `num_fluids` defines the total number of fluids defined in each of the patches. The number has to be a positive integer.

‎docs/documentation/readme.md‎

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- [Getting Started](getting-started.md)
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- [Testing MFC](testing.md)
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- [Case Files](case.md)
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- [Example Cases](examples.md)
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- [Running MFC](running.md)
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- [Flow Visualisation](visualisation.md)
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- [MFC's Authors](authors.md)

‎docs/examples.sh‎

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#!/bin/bash
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set -e
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examples_md="$1/docs/documentation/examples.md"
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rm "$examples_md" || true
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echo -e "# Example Cases\n" > "$examples_md"
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for casedir in $(find "$1/examples/" -maxdepth 1 -type d); do
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casename="$(basename $casedir)"
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if [ "$casename" == "examples" ]; then
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continue
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fi
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if [ -f "$casedir/README.md" ]; then
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sed -e "s/\.png/-$casename\.png/g" "$casedir/README.md" | sed 's/^#/##/g' >> "$examples_md"
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echo "" >> "$examples_md"
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for png in $(find "$casedir" -maxdepth 1 -name "*.png"); do
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cp "$png" "$1/docs/documentation/$(basename $png | sed s/\.png//g)-$casename.png"
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done
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fi
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done

‎examples/1D_shuosher/README.md‎

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# Shu-Osher problem (1D)
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Reference: https://arxiv.org/pdf/2110.05461.pdf.
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## Initial Condition
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![Initial Condition](initial.png)
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## Result
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![Result](result.png)

‎examples/1D_shuosher/case.py‎

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#!/usr/bin/env python3
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import math
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import json
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# Numerical setup
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Nx = 1000
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dx = 1./(1.*(Nx+1))
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Tend, Nt = 1.8, 20000
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mydt = Tend/(1.*Nt)
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# Configuring case dictionary
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print(json.dumps({
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# Logistics ================================================================
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'run_time_info' : 'T',
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# ==========================================================================
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# Computational Domain Parameters ==========================================
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'x_domain%beg' : -5.,
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'x_domain%end' : 5. ,
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'm' : Nx,
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'n' : 0,
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'p' : 0,
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'dt' : mydt,
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't_step_start' : 0,
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't_step_stop' : int(Nt),
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't_step_save' : int(math.ceil(Nt/10.0)),
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# ==========================================================================
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# Simulation Algorithm Parameters ==========================================
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'num_patches' : 2,
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'model_eqns' : 2,
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'alt_soundspeed' : 'F',
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'num_fluids' : 1,
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'adv_alphan' : 'T',
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'mpp_lim' : 'F',
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'mixture_err' : 'F',
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'time_stepper' : 3,
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'weno_order' : 5,
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'weno_eps' : 1.E-16,
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'mapped_weno' : 'T',
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'null_weights' : 'F',
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'mp_weno' : 'F',
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'riemann_solver' : 2,
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'wave_speeds' : 1,
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'avg_state' : 2,
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'bc_x%beg' : -3,
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'bc_x%end' : -3,
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# ==========================================================================
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# Formatted Database Files Structure Parameters ============================
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'format' : 1,
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'precision' : 2,
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'prim_vars_wrt' :'T',
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'parallel_io' :'F',
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# ==========================================================================
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# Background to cover whole domain with basic line patch
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# Patch 1 Left (-5 < x < -4) ===============================================
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'patch_icpp(1)%geometry' : 1,
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'patch_icpp(1)%x_centroid' : -4.5,
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'patch_icpp(1)%length_x' : 1.,
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'patch_icpp(1)%vel(1)' : 2.629369,
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'patch_icpp(1)%pres' : 10.3333,
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'patch_icpp(1)%alpha_rho(1)' : 3.957143,
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'patch_icpp(1)%alpha(1)' : 1.,
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# ==========================================================================
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# One anlytic patch to take care of -4 < x < 5
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# Patch 2 Analytic =========================================================
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'patch_icpp(2)%geometry' : 15,
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'patch_icpp(2)%x_centroid' : 0.5,
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'patch_icpp(2)%length_x' : 9.,
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'patch_icpp(2)%vel(1)' : 0.,
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'patch_icpp(2)%pres' : 1.,
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'patch_icpp(2)%alpha_rho(1)' : '1 + 0.2*sin(5*x)',
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'patch_icpp(2)%alpha(1)' : 1.,
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# ==========================================================================
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# Fluids Physical Parameters ===============================================
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'fluid_pp(1)%gamma' : 1.E+00/(1.4-1.E+00),
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'fluid_pp(1)%pi_inf' : 0.0,
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# ==========================================================================
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}))
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# ==============================================================================

‎examples/1D_shuosher/initial.png‎

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‎examples/1D_shuosher/result.png‎

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