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hyeoksu-leeHyeoksu LeeHyeoksu LeeHyeoksu LeeHyeoksu Lee
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Operator splitting, adaptive time stepping, and other fixes for mixing layer and bubbles (#285)
Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Hyeoksu Lee <[email protected]> Co-authored-by: Anand Radhakrishnan <[email protected]> Co-authored-by: Anand Radhakrishnan <[email protected]> Co-authored-by: Anand Radhakrishnan <[email protected]> Co-authored-by: Anand <[email protected]>
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‎docs/documentation/case.md‎

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@@ -79,6 +79,7 @@ There are multiple sets of parameters that must be specified in the python input
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8. [(Optional) Ensemble-Averaged Bubble Model Parameters](#8-ensemble-averaged-bubble-model)
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9. [(Optional) Velocity Field Setup Parameters](#9-velocity-field-setup)
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10. [(Optional) Phase Change Parameters](#10-Phase-Change-Model)
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11. [(Optional) Artificial Mach Number Parameters](#11-artificial-Mach-number)
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Items 7, 8, 9, and 10 are optional sets of parameters that activate the acoustic source model, ensemble-averaged bubble model, initial velocity field setup, and phase change, respectively.
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Definition of the parameters is described in the following subsections.
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| `model_eqns` | Integer | Multicomponent model: [1] $\Gamma/\Pi_\infty$; [2] 5-equation; [3] 6-equation\\%;%[4] 4-equation |
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| `alt_soundspeed` * | Logical | Alternate sound speed and $K \nabla \cdot u$ for 5-equation model |
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| `adv_alphan` | Logical | Equations for all $N$ volume fractions (instead of $N-1$) |
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| `adv_n` | Logical | Solving directly for the number density (in the method of classes) and compute void fraction from the number density |
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| `mpp_lim` | Logical | Mixture physical parameters limits |
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| `mixture_err` | Logical | Mixture properties correction |
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| `time_stepper` | Integer | Runge-Kutta order [1-3] |
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| `time_stepper` | Integer | Runge--Kutta order [1-3] |
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| `adap_dt` | Loginal | Strang splitting scheme with adaptive time stepping |
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| `weno_order` | Integer | WENO order [1,3,5] |
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| `weno_eps` | Real | WENO perturbation (avoid division by zero) |
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| `mapped_weno` | Logical | WENO with mapping of nonlinear weights |
@@ -396,13 +399,17 @@ $$ \alpha_N=1-\sum^{N-1}_{i=1} \alpha_i $$
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where $\alpha_i$ is the void fraction of $i$-th component.
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When a single-component flow is simulated, it requires that `adv_alphan = 'T'`.
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- `adv_n` activates the direct computation of number density by the Riemann solver instead of computing number density from the void fraction in the method of classes.
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- `mpp_lim` activates correction of solutions to avoid a negative void fraction of each component in each grid cell, such that $\alpha_i>\varepsilon$ is satisfied at each time step.
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- `mixture_err` activates correction of solutions to avoid imaginary speed of sound at each grid cell.
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- `time_stepper` specifies the order of the Runge-Kutta (RK) time integration scheme that is used for temporal integration in simulation, from the 1st to 5th order by corresponding integer.
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Note that `time_stepper = 3` specifies the total variation diminishing (TVD), third order RK scheme ([Gottlieb and Shu, 1998](references.md#Gottlieb98)).
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- `adap_dt` activates the Strang operator splitting scheme which splits flux and source terms in time marching, and an adaptive time stepping strategy is implemented for the source term. It requires `bubbles = 'T'`, `polytropic = 'T'`, `adv_n = 'T'` and `time_stepper = 3`.
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- `weno_order` specifies the order of WENO scheme that is used for spatial reconstruction of variables by an integer of 1, 3, and 5, that correspond to the 1st, 3rd, and 5th order, respectively.
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- `weno_eps` specifies the lower bound of the WENO nonlinear weights.
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- `vel_profile` activates setting the mean streamwise velocity to hyperbolic tangent profile. This option works only for 2D and 3D cases.
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- `instability_wave` activates the perturbation of initial velocity by instability waves obtained from linear stability analysis for a mixing layer with hyperbolic tangent mean streamwise velocity profile.
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This option only works for 2D and 3D cases, together with `vel_profile = 'T'`.
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- `instability_wave` activates the perturbation of initial velocity by instability waves obtained from linear stability analysis for a mixing layer with hyperbolic tangent mean streamwise velocity profile. This option only works for `n > 0`, `bc_y%[beg,end] = -5`, and `vel_profile = 'T'`.
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### 11. Phase Change Model
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| Parameter | Type | Description |
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- `ptgalpha_eps` Specifies the tolerance used for the Newton Solvers used in the pTg-equilibrium model.
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### 11. Artificial Mach Number
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| Parameter | Type | Description |
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| ---: | :----: | :--- |
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| `pi_fac` | Real | Ratio of artificial and true `pi_\infty` values|
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- `pi_fac` specifies the ratio of artificial and true `pi_\infty` values (`=` artificial `pi_\infty` / true `pi_\infty`). This parameter enables the use of true `pi_\infty` in bubble dynamics models, when the `pi_\infty` given in the `case.py` file is an artificial value.
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## Enumerations
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### Boundary conditions

‎examples/0D_bubblecollapse_adap/case.py‎

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#!/usr/bin/env python2
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import math
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import json
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# FLUID PROPERTIES ============================================================
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# Water
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n_tait = 7.1
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B_tait = 306.E+06
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rho0 = 1.E+03
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mul0 = 1.002E-03
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ss = 0.07275
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pv = 2.3388E+03
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# Vapor
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gamma_v = 1.33
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M_v = 18.02
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mu_v = 0.8816E-05
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k_v = 0.019426
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# Air
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gamma_n = 1.4
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M_n = 28.97
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mu_n = 1.8E-05
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k_n = 0.02556
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# REFERENCE VALUES ============================================================
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R0ref = 50.E-06
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x0 = R0ref
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p0 = 8236. # for Ca = 1 in mixing layer scale
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u0 = math.sqrt( p0/rho0 )
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patm = 1.
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cact = math.sqrt(n_tait*(p0+B_tait)/rho0)
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# NONDIMENSIONAL NUMBERS ======================================================
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Ca = (p0 - pv)/(rho0*(u0**2.)) # Cavitation number
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We = rho0*(u0**2.)*R0ref/ss # Weber number
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Re_inv = mul0/(rho0*u0*R0ref) # Inv. bubble Reynolds number
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# BUBBLES =====================================================================
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vf0 = 1e-5
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nb = 1
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# DOMAIN ======================================================================
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Nx = 30
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Ldomain = 20.E-03
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L = Ldomain/x0
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dx = L/float(Nx+1)
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# TIME STEPS ==================================================================
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Tfinal = 0.05
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Nt = int(5e2+1)
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t_save = 1
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dt = Tfinal/(Nt-1)
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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' : -0.5*L,
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'x_domain%end' : 0.5*L,
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'stretch_x' : 'F',
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'cyl_coord' : 'F',
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'm' : Nx,
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'n' : 0,
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'p' : 0,
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'dt' : dt,
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't_step_start' : 0,
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't_step_stop' : Nt,
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't_step_save' : t_save,
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# ==========================================================
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# Simulation Algorithm Parameters ==========================
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'num_patches' : 1,
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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' : 'T',
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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' : -1,
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'bc_x%end' : -1,
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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' :'T',
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'fd_order' : 1,
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# ==========================================================
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# Patch 1 _ Background =====================================
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'patch_icpp(1)%geometry' : 1,
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'patch_icpp(1)%x_centroid' : 0.,
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'patch_icpp(1)%length_x' : L,
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'patch_icpp(1)%vel(1)' : 0.,
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'patch_icpp(1)%pres' : 1000.,
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'patch_icpp(1)%alpha_rho(1)' : (1.-vf0),
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'patch_icpp(1)%alpha(1)' : vf0,
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'patch_icpp(1)%r0' : 1.,
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'patch_icpp(1)%v0' : 0.,
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# ==========================================================
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# Non-polytropic gas compression model AND/OR Tait EOS =====
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'pref' : p0,
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'rhoref' : rho0,
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# ==========================================================
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# Bubbles ==================================================
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'bubbles' : 'T',
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'bubble_model' : 2,
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# Nondimensional numbers
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'Ca' : Ca,
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'Web' : We,
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'Re_inv' : Re_inv,
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# adv_n
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'adv_n' : 'T',
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# adap_dt
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'adap_dt' : 'T',
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# Gas compression model
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'polytropic' : 'T',
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'thermal' : 1,
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# Polydispersity
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'polydisperse' : 'F',
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'nb' : nb,
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# QBMM
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'qbmm' : 'F',
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# ==========================================================
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# Fluids Physical Parameters ===============================
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# Surrounding liquid
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'fluid_pp(1)%gamma' : 1.E+00/(n_tait-1.E+00),
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'fluid_pp(1)%pi_inf' : n_tait*(B_tait/p0)/(n_tait-1.),
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'fluid_pp(1)%ss' : ss,
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'fluid_pp(1)%pv' : pv,
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# Last fluid_pp is always reserved for bubble gas state ===
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# if applicable ==========================================
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'fluid_pp(2)%gamma' : 1./(gamma_n-1.),
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'fluid_pp(2)%pi_inf' : 0.0E+00,
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# ==========================================================
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}))
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# ==============================================================================

‎examples/2D_mixing_artificial_Ma/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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# FLUID PROPERTIES (WATER, VAPOR & AIR) ========================================
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# Water
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rho_w = 1.E+03 # [kg/m3] density of water
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gamma_w = 7.1 # [1] specific heat ratio
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pi_inf_w = 3.06E+08 # [N/m2] water stiffness
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# ==============================================================================
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# REFERENCE VALUES =============================================================
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x_ref = 0.002475 # [m] initial vorticity thickness
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u_ref = 3.4343 # [m/s] upper stream velocity
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# ==============================================================================
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# NON-DIMENSIONAL NUMBERS ======================================================
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Re = 50. # [1] Reynolds number based on the upper stream
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# velocity and the initial vorticity thickness
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# ==============================================================================
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# SPEED OF SOUND ===============================================================
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pres = 8236. # [N/m2] pressure of water
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c_w = math.sqrt(gamma_w*(pres+pi_inf_w)/rho_w)
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# ==============================================================================
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# MODIFIED PROPERTIES FOR ARTIFICIAL MACH NUMBER ==============================
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Ma_t = 0.1 # [1] target Mach number
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pi_fac = (rho_w*u_ref**2/(gamma_w*Ma_t**2)-pres)/pi_inf_w
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pi_inf_w = pi_inf_w*pi_fac
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c_w = math.sqrt(gamma_w*(pres+pi_inf_w)/rho_w)
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# =============================================================================
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# SIMULATION SETUP ============================================================
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# Domain size
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Lx = 59.0
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Ly = 59.0
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# Number of grid cells
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Nx = 191
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Ny = 191
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# Grid spacing
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dx = Lx/float(Nx+1)
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dy = Ly/float(Ny+1)
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# Time advancement
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cfl = 5e-1
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T = 20.
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dt = cfl*dx/(1.+c_w/u_ref)
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Ntfinal = int(T/dt)
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Ntstart = 0
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Nfiles = 20
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t_save = int(math.ceil((Ntfinal-0)/float(Nfiles)))
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Nt = t_save*Nfiles
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t_step_start = Ntstart
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t_step_stop = int(Nt)
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# ==============================================================================
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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' : 0.,
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'x_domain%end' : Lx,
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'y_domain%beg' : -Ly/2.,
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'y_domain%end' : Ly/2.,
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'm' : Nx,
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'n' : Ny,
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'p' : 0,
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'dt' : dt,
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't_step_start' : t_step_start,
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't_step_stop' : t_step_stop,
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't_step_save' : t_save,
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# ==========================================================================
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# Simulation Algorithm Parameters ==========================================
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'num_patches' : 1,
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'model_eqns' : 2,
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'num_fluids' : 1,
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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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'weno_Re_flux' : 'T',
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'mapped_weno' : 'T',
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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' : -1,
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'bc_x%end' : -1,
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'bc_y%beg' : -5,
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'bc_y%end' : -5,
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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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'cons_vars_wrt' :'T',
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'prim_vars_wrt' :'T',
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'parallel_io' :'T',
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'fd_order' : 1,
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'omega_wrt(3)' :'T',
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# ==========================================================================
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# Patch 1 ==================================================================
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'patch_icpp(1)%geometry' : 3,
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'patch_icpp(1)%x_centroid' : Lx/2.,
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'patch_icpp(1)%y_centroid' : 0.,
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'patch_icpp(1)%length_x' : Lx,
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'patch_icpp(1)%length_y' : Ly,
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'patch_icpp(1)%alpha_rho(1)' : 1.,
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'patch_icpp(1)%alpha(1)' : 1.,
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'patch_icpp(1)%vel(1)' : 1.,
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'patch_icpp(1)%vel(2)' : 0.,
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'patch_icpp(1)%pres' : pres/(rho_w*u_ref**2),
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# ==========================================================================
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# Mixing layer === =========================================================
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'vel_profile' : 'T',
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'instability_wave' : 'T',
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# ==========================================================================
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# Artificial Mach number ===================================================
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'pi_fac' : pi_fac,
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# ==========================================================================
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# Fluids Physical Parameters ===============================================
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'fluid_pp(1)%gamma' : 1.E+00/(gamma_w-1.E+00),
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'fluid_pp(1)%pi_inf' : gamma_w*(pi_inf_w/(rho_w*u_ref**2))/(gamma_w-1.E+00),
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'fluid_pp(1)%Re(1)' : Re,
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# =========================================================================
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}))
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# ==============================================================================

‎src/common/m_helper.fpp‎

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use m_global_parameters !< Definitions of the global parameters
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use m_mpi_common !< MPI modules
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use ieee_arithmetic !< For checking NaN
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! ==========================================================================
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implicit none

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