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‎documentation/md_case.html‎

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<h2><a class="anchor" id="autotoc_md16"></a>
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6. Simulation Algorithm</h2>
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<p><br />
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| Parameter . | Type | Description | | &mdash;: . | :-&mdash;: | :&mdash; | | <code>bc_[x,y,z]%beg[end]</code> . | Integer | Beginning [ending] boundary condition in the $[x,y,z]$-direction (negative integer, see table Boundary Conditions) | | <code>bc_[x,y,z]%vb[1,2,3]</code>‡. | Real | Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]%beg</code> | | <code>bc_[x,y,z]%ve[1,2,3]</code>‡. | Real | Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]%end</code> | | <code>model_eqns</code> | Integer | Multicomponent model: [1] $\Gamma/\Pi_\infty$; [2] 5-equation; [3] 6-equation; [4] 4-equation | | <code>alt_soundspeed</code> * | Logical | Alternate sound speed and $K \nabla \cdot u$ for 5-equation model | | <code>adv_n</code> | Logical | Solving directly for the number density (in the method of classes) and compute void fraction from the number density | | <code>mpp_lim</code> | Logical | Mixture physical parameters limits | | <code>mixture_err</code> | Logical | Mixture properties correction | | <code>time_stepper</code> | Integer | Runge&ndash;Kutta order [1-3] | | <code>adap_dt</code> | Logical | Strang splitting scheme with adaptive time stepping | | <code>recon_type</code> | Integer | Reconstruction Type: [1] WENO; [2] MUSCL | | <code>adap_dt_tol</code> | Real | Tolerance for adaptive time stepping in Strang splitting scheme| | <code>adap_dt_max_iters</code> | Integer | Max iteration for adaptive time stepping in Strang splitting scheme | | <code>weno_order</code> | Integer | WENO order [1,3,5] | | <code>weno_eps</code> | Real | WENO perturbation (avoid division by zero) | | <code>mapped_weno</code> | Logical | WENO-M (WENO with mapping of nonlinear weights) | | <code>wenoz</code> | Logical | WENO-Z | | <code>wenoz_q</code> | Real | WENO-Z power parameter q (only for WENO7) | | <code>teno</code> | Logical | TENO (Targeted ENO) | | <code>teno_CT</code> | Real | TENO threshold for smoothness detection | | <code>null_weights</code> | Logical | Null WENO weights at boundaries | | <code>mp_weno</code> | Logical | Monotonicity preserving WENO | | <code>muscl_order</code> | Integer | MUSCL order [1,2] | | <code>muscl_lim</code> | Integer | MUSCL Slope Limiter: [1] minmod; [2] monotonized central; [3] Van Albada; [4] Van Leer; [5] SUPERBEE | | <code>int_comp</code> | Logical | THINC Interface Compression | | <code>ic_eps</code> | Real | Interface compression threshold (default: 1e-4) | | <code>ic_beta</code> | Real | Interface compression sharpness parameter (default: 1.6) | | <code>riemann_solver</code> | Integer | Riemann solver algorithm: [1] HLL*; [2] HLLC; [3] Exact*; [4] HLLD (only for MHD) | | <code>low_Mach</code> | Integer | Low Mach number correction for HLLC Riemann solver: [0] None; [1] Pressure (Chen et al. 2022); [2] Velocity (Thornber et al. 2008) | | <code>avg_state</code> | Integer | Averaged state evaluation method: [1] Roe average*; [2] Arithmetic mean | | <code>wave_speeds</code> | Integer | Wave-speed estimation: [1] Direct (Batten et al. 1997); [2] Pressure-velocity* (Toro 1999) | | <code>weno_Re_flux</code> | Logical | Compute velocity gradient using scalar divergence theorem | | <code>weno_avg</code> | Logical | Arithmetic mean of left and right, WENO-reconstructed, cell-boundary values | | <code>dt</code> | Real | Time step size | | <code>t_step_start</code> | Integer | Simulation starting time step | | <code>t_step_stop</code> | Integer | Simulation stopping time step | | <code>t_step_save</code> | Integer | Frequency to output data | | <code>t_step_print</code> | Integer | Frequency to print the current step number to standard output (default 1) | | <code>cfl_adap_dt</code> | Logical | CFL based adaptive time-stepping | | <code>cfl_const_dt</code> | Logical | CFL based non-adaptive time-stepping | | <code>cfl_target</code> | Real | Specified CFL value | | <code>n_start</code> | Integer | Save file from which to start simulation | | <code>t_save</code> | Real | Time duration between data output | | <code>t_stop</code> | Real | Simulation stop time | | <code>surface_tension</code> | Logical | Activate surface tension | | <code>viscous</code> | Logical | Activate viscosity | | <code>hypoelasticity</code> | Logical | Activate hypoelasticity* | | <code>igr</code> | Logical | Enable solution via information geometric regularization (IGR) <a class="el" href="md_references.html">Cao (2024)</a> | | <code>igr_order</code> | Integer | Order of reconstruction for IGR [3,5] | | <code>alf_factor</code> | Real | Alpha factor for IGR entropic pressure (default 10) | | <code>igr_pres_lim</code> | Logical | Limit IGR pressure to avoid negative values (default F) | | <code>igr_iter_solver</code> | Integer | Solution method for IGR elliptic solve [1] Jacobi [2] Gauss-Seidel | | <code>num_igr_iters</code> | Integer | Number of iterations for for the IGR elliptic solve (default 2) | | <code>num_igr_warm_start_iters</code> | Integer | Number of iterations for the IGR elliptic solve at the first time step (default 50) |</p>
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<table class="markdownTable">
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<tr class="markdownTableHead">
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<th class="markdownTableHeadRight">Parameter </th><th class="markdownTableHeadCenter">Type </th><th class="markdownTableHeadLeft">Description </th></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>bc_[x,y,z]%beg[end]</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Beginning [ending] boundary condition in the $[x,y,z]$-direction (negative integer, see table Boundary Conditions) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>bc_[x,y,z]%vb[1,2,3]</code>‡ </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]%beg</code> </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>bc_[x,y,z]%ve[1,2,3]</code>‡ </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Velocity in the (x,1), (y, 2), (z,3) direction applied to <code>bc_[x,y,z]%end</code> </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>model_eqns</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Multicomponent model: [1] $\Gamma/\Pi_\infty$; [2] 5-equation; [3] 6-equation; [4] 4-equation </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>alt_soundspeed</code> * </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Alternate sound speed and $K \nabla \cdot u$ for 5-equation model </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>adv_n</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Solving directly for the number density (in the method of classes) and compute void fraction from the number density </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>mpp_lim</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Mixture physical parameters limits </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>mixture_err</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Mixture properties correction </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>time_stepper</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Runge&ndash;Kutta order [1-3] </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>adap_dt</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Strang splitting scheme with adaptive time stepping </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>recon_type</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Reconstruction Type: [1] WENO; [2] MUSCL </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>adap_dt_tol</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Tolerance for adaptive time stepping in Strang splitting scheme </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>adap_dt_max_iters</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Max iteration for adaptive time stepping in Strang splitting scheme </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>weno_order</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">WENO order [1,3,5] </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>weno_eps</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">WENO perturbation (avoid division by zero) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>mapped_weno</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">WENO-M (WENO with mapping of nonlinear weights) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>wenoz</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">WENO-Z </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>wenoz_q</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">WENO-Z power parameter q (only for WENO7) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>teno</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">TENO (Targeted ENO) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>teno_CT</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">TENO threshold for smoothness detection </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>null_weights</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Null WENO weights at boundaries </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>mp_weno</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Monotonicity preserving WENO </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>muscl_order</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">MUSCL order [1,2] </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>muscl_lim</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">MUSCL Slope Limiter: [1] minmod; [2] monotonized central; [3] Van Albada; [4] Van Leer; [5] SUPERBEE </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>int_comp</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">THINC Interface Compression </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>ic_eps</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Interface compression threshold (default: 1e-4) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>ic_beta</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Interface compression sharpness parameter (default: 1.6) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>riemann_solver</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Riemann solver algorithm: [1] HLL*; [2] HLLC; [3] Exact*; [4] HLLD (only for MHD) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>low_Mach</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Low Mach number correction for HLLC Riemann solver: [0] None; [1] Pressure (Chen et al. 2022); [2] Velocity (Thornber et al. 2008) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>avg_state</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Averaged state evaluation method: [1] Roe average*; [2] Arithmetic mean </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>wave_speeds</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Wave-speed estimation: [1] Direct (Batten et al. 1997); [2] Pressure-velocity* (Toro 1999) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>weno_Re_flux</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Compute velocity gradient using scalar divergence theorem </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>weno_avg</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Arithmetic mean of left and right, WENO-reconstructed, cell-boundary values </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>dt</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Time step size </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>t_step_start</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Simulation starting time step </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>t_step_stop</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Simulation stopping time step </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>t_step_save</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Frequency to output data </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>t_step_print</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Frequency to print the current step number to standard output (default 1) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>cfl_adap_dt</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">CFL based adaptive time-stepping </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>cfl_const_dt</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">CFL based non-adaptive time-stepping </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>cfl_target</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Specified CFL value </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>n_start</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Save file from which to start simulation </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>t_save</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Time duration between data output </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>t_stop</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Simulation stop time </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>surface_tension</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Activate surface tension </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>viscous</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Activate viscosity </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>hypoelasticity</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Activate hypoelasticity* </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>igr</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Enable solution via information geometric regularization (IGR) <a class="el" href="md_references.html">Cao (2024)</a> </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>igr_order</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Order of reconstruction for IGR [3,5] </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>alf_factor</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Alpha factor for IGR entropic pressure (default 10) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>igr_pres_lim</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Limit IGR pressure to avoid negative values (default F) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>igr_iter_solver</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Solution method for IGR elliptic solve [1] Jacobi [2] Gauss-Seidel </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>num_igr_iters</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Number of iterations for for the IGR elliptic solve (default 2) </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>num_igr_warm_start_iters</code> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Number of iterations for the IGR elliptic solve at the first time step (default 50) </td></tr>
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</table>
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<ul>
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<li>* Options that work only with <code>model_eqns = 2</code>.</li>
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<li>† Options that work only with <code>cyl_coord = 'F'</code>.</li>

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