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MHD & RMHD (#809)
* B equations added * 1D Brio Wu works * 2D Brio Wu works * add Orszag Tang test * 3D works; add case folder * add Powell * HLLD as copy of HLL * 1D & 2D HLLD works * 3D RMHD works * format and add cases * more examples * add tests * minor clean ups * case opt * golden for examples * docs and checker * small GPU fix * fix tests * exclude HLLD from single-precision tests * fix prim vs cons density * fix GPU tests * regenerate rmhd golden * clean * fix merge bug * fix unassigned flux_src_rs (evident in intel compiler hlld tests) * fix ieee module bug for intel * remove case * fix hlld example test * remove magic number * remove unicode * riemann states type * fix gpu bug * remove Bxb Bxe * update README * fix frontier bug * fix frontier bug 2 * fix frontier bug 3 * fix gpu case-opt * refactor and clean up --------- Co-authored-by: Spencer Bryngelson <sbryngelson@gmail.com>
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‎README.md

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@@ -132,6 +132,8 @@ They are organized below.
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* Ideal and stiffened gas equations of state
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* Body forces
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* Acoustic wave generation (one- and two-way sound sources)
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* Magnetohydrodynamics (MHD)
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* Relativistic Magnetohydrodynamics (RMHD)
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</details>
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### Numerics
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* WENO variants: WENO-JS, WENO-M, WENO-Z, TENO
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* Monotonicity-preserving reconstructions
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* Reliable handling of large density ratios
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* Exact and approximate (e.g., HLL, HLLC) Riemann solvers
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* Exact and approximate (e.g., HLL, HLLC, HLLD) Riemann solvers
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* Boundary conditions
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* Periodic, reflective, extrapolation/Neumann
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* Slip and no-slip

‎docs/documentation/case.md

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@@ -372,7 +372,7 @@ Details of implementation of viscosity in MFC can be found in [Coralic (2015)](r
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| `teno_CT` | Real | TENO threshold for smoothness detection |
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| `null_weights` | Logical | Null WENO weights at boundaries |
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| `mp_weno` | Logical | Monotonicity preserving WENO |
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| `riemann_solver` | Integer | Riemann solver algorithm: [1] HLL*; [2] HLLC; [3] Exact* |
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| `riemann_solver` | Integer | Riemann solver algorithm: [1] HLL*; [2] HLLC; [3] Exact*; [4] HLLD (only for MHD) |
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| `low_Mach` | Integer | Low Mach number correction for HLLC Riemann solver: [0] None; [1] Pressure (Chen et al. 2022); [2] Velocity (Thornber et al. 2008) |
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| `avg_state` | Integer | Averaged state evaluation method: [1] Roe average*; [2] Arithmetic mean |
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| `wave_speeds` | Integer | Wave-speed estimation: [1] Direct (Batten et al. 1997); [2] Pressure-velocity* (Toro 1999) |
@@ -450,6 +450,7 @@ It is recommended to set `weno_eps` to $10^{-6}$ for WENO-JS, and to $10^{-40}$
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- `riemann_solver` specifies the choice of the Riemann solver that is used in simulation by an integer from 1 through 3.
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`riemann_solver = 1`, `2`, and `3` correspond to HLL, HLLC, and Exact Riemann solver, respectively ([Toro, 2013](references.md#Toro13)).
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`riemann_solver = 4` is only for MHD simulations. It resolves 5 of the full seven-wave structure of the MHD equations ([Miyoshi and Kusano, 2005](references.md#Miyoshi05)).
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- `low_Mach` specifies the choice of the low Mach number correction scheme for the HLLC Riemann solver. `low_Mach = 0` is default value and does not apply any correction scheme. `low_Mach = 1` and `2` apply the anti-dissipation pressure correction method ([Chen et al., 2022](references.md#Chen22)) and the improved velocity reconstruction method ([Thornber et al., 2008](references.md#Thornber08)). This feature requires `riemann_solver = 2` and `model_eqns = 2`.
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@@ -848,7 +849,34 @@ $$ a_{x[y,z]} = g_{x[y,z]} + k_{x[y,z]}\sin\left(w_{x[y,z]}t + p_{x[y,z]}\right)
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By convention, positive accelerations in the `x[y,z]` direction are in the positive `x[y,z]` direction.
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### 14. Cylindrical Coordinates
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### 14. Magnetohydrodynamics (MHD)
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| Parameter | Type | Description |
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| ---: | :---: | :--- |
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| `mhd` | Logical | Enable ideal MHD simulation |
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| `relativity` | Logical | Enable relativistic MHD simulation |
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| `powell` | Logical | Enable Powell's method for solenoidal constraint |
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| `fd_order` | Integer | Finite difference order for Powell's method |
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| `Bx[y,z]` | Real | Initial magnetic field in the x[y,z] direction |
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| `Bx0` | Real | Constant magnetic field in the x direction (1D only)|
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- `mhd` is currently only available for single-component flows and 5-equation model. Its compatibility with most other features is work in progress.
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- `relativity` only works for `mhd` enabled and activates relativistic MHD (RMHD) simulation.
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- `powell` activates Powell's eight-wave method to impose the solenoidal constraint in the MHD simulation [Powell (1994)](references.md#Powell94). It should not be used in conjunction with HLLD (`riemann_solver = 4`).
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- `fd_order` specifies the finite difference order for computing the RHS of the Powell's method. `fd_order = 1`, `2`, and `4` are allowed.
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- `Bx0` is only used in 1D simulations to specify the constant magnetic field in the x direction. It must be specified in 1D simulations. `Bx` must not be used in 1D simulations.
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- `Bx`, `By`, and `Bz` are used to specify the initial magnetic field in the x, y, and z directions, respectively. They must be specified in all 1D/2D/3D MHD simulations, with the exception of `Bx` in 1D simulations.
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Note: In 1D/2D/3D simulations, all three velocity components are treated as state variables and must be specified in the case file.
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Note: For relativistic flow, the conservative and primitive densities are different. `rho_wrt` outputs the primitive (rest mass) density.
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### 15. Cylindrical Coordinates
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When ``cyl_coord = 'T'`` is set in 3D the following constraints must be met:
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‎docs/documentation/references.md

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- <a id="Tiwari13">Tiwari, A., Freund, J. B., and Pantano, C. (2013). A diffuse interface model with immiscibility preservation. Journal of computational physics, 252:290–309.</a>
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- <a id="Toro13">Toro, E. F. (2013). Riemann solvers and numerical methods for fluid dynamics: a practical introduction. Springer Science & Business Media.</a>
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- <a id="Miyoshi05">Miyoishi, T., and Kusano, K. (2005). A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics. Journal of Computational Physics, 208(1), 315-344.</a>
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- <a id="Powell94">Powell, K. G. (1994). An approximate Riemann solver for magnetohydrodynamics: (That works in more than one dimension). In Upwind and high-resolution schemes (pp. 570-583). Springer.</a>

‎examples/1D_brio_wu/case.py

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#!/usr/bin/env python3
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import json
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# An upwind differencing scheme for the equations of ideal magnetohydrodynamics
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# M. Brio and C. C. Wu
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# Configuring case dictionary
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print(
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json.dumps(
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{
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# Logistics
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"run_time_info": "T",
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# Computational Domain Parameters
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"x_domain%beg": 0,
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"x_domain%end": 1.0,
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"m": 800,
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"n": 0,
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"p": 0,
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"dt": 0.0002,
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"t_step_start": 0,
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"t_step_stop": 1000,
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"t_step_save": 100,
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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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"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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"mapped_weno": "T",
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"weno_eps": 1.0e-16,
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"null_weights": "F",
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"mp_weno": "F",
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"riemann_solver": 1,
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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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# 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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"rho_wrt": "T",
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"parallel_io": "T",
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# MHD
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"mhd": "T",
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"Bx0": 0.75,
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# Patch 1 Left
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"patch_icpp(1)%geometry": 1,
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"patch_icpp(1)%x_centroid": 0.25,
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"patch_icpp(1)%length_x": 0.5,
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"patch_icpp(1)%vel(1)": 0.0,
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"patch_icpp(1)%vel(2)": 0.0,
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"patch_icpp(1)%vel(3)": 0.0,
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"patch_icpp(1)%pres": 1.0,
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"patch_icpp(1)%By": 1.0,
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"patch_icpp(1)%Bz": 0.0,
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"patch_icpp(1)%alpha_rho(1)": 1.0,
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"patch_icpp(1)%alpha(1)": 1.0,
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# Patch 2 Right
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"patch_icpp(2)%geometry": 1,
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"patch_icpp(2)%x_centroid": 0.75,
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"patch_icpp(2)%length_x": 0.5,
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"patch_icpp(2)%vel(1)": 0.0,
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"patch_icpp(2)%vel(2)": 0.0,
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"patch_icpp(2)%vel(3)": 0.0,
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"patch_icpp(2)%pres": 0.1,
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"patch_icpp(2)%By": -1.0,
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"patch_icpp(2)%Bz": 0.0,
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"patch_icpp(2)%alpha_rho(1)": 0.125,
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"patch_icpp(2)%alpha(1)": 1.0,
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# Fluids Physical Parameters
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"fluid_pp(1)%gamma": 1.0e00 / (2.0e00 - 1.0e00),
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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_brio_wu_hlld/case.py

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#!/usr/bin/env python3
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import json
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# An upwind differencing scheme for the equations of ideal magnetohydrodynamics
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# M. Brio and C. C. Wu
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# Note: HLLD is not used in the paper
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# Configuring case dictionary
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print(
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json.dumps(
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{
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# Logistics
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"run_time_info": "T",
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# Computational Domain Parameters
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"x_domain%beg": 0,
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"x_domain%end": 1.0,
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"m": 800,
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"n": 0,
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"p": 0,
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"dt": 0.0002,
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"t_step_start": 0,
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"t_step_stop": 1000,
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"t_step_save": 100,
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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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"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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"mapped_weno": "T",
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"weno_eps": 1.0e-16,
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"null_weights": "F",
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"mp_weno": "F",
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"riemann_solver": 4,
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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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# 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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"rho_wrt": "T",
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"parallel_io": "T",
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# MHD
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"mhd": "T",
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"Bx0": 0.75,
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# Patch 1 Left
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"patch_icpp(1)%geometry": 1,
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"patch_icpp(1)%x_centroid": 0.25,
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"patch_icpp(1)%length_x": 0.5,
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"patch_icpp(1)%vel(1)": 0.0,
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"patch_icpp(1)%vel(2)": 0.0,
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"patch_icpp(1)%vel(3)": 0.0,
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"patch_icpp(1)%pres": 1.0,
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"patch_icpp(1)%By": 1.0,
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"patch_icpp(1)%Bz": 0.0,
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"patch_icpp(1)%alpha_rho(1)": 1.0,
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"patch_icpp(1)%alpha(1)": 1.0,
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# Patch 2 Right
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"patch_icpp(2)%geometry": 1,
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"patch_icpp(2)%x_centroid": 0.75,
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"patch_icpp(2)%length_x": 0.5,
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"patch_icpp(2)%vel(1)": 0.0,
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"patch_icpp(2)%vel(2)": 0.0,
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"patch_icpp(2)%vel(3)": 0.0,
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"patch_icpp(2)%pres": 0.1,
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"patch_icpp(2)%By": -1.0,
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"patch_icpp(2)%Bz": 0.0,
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"patch_icpp(2)%alpha_rho(1)": 0.125,
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"patch_icpp(2)%alpha(1)": 1.0,
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# Fluids Physical Parameters
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"fluid_pp(1)%gamma": 1.0e00 / (2.0e00 - 1.0e00),
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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_brio_wu_rmhd/case.py

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#!/usr/bin/env python3
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import json
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# An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics
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# A. Mignone and G. Bodo
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# Problem 1 Figure 3
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# Configuring case dictionary
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print(
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json.dumps(
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{
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# Logistics
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"run_time_info": "T",
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# Computational Domain Parameters
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"x_domain%beg": 0,
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"x_domain%end": 1.0,
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"m": 1600,
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"n": 0,
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"p": 0,
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"dt": 0.0002,
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"t_step_start": 0,
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"t_step_stop": 2000,
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"t_step_save": 100,
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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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"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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"mapped_weno": "T",
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"weno_eps": 1.0e-16,
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"null_weights": "F",
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"mp_weno": "F",
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"riemann_solver": 1,
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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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# 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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"rho_wrt": "T",
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"parallel_io": "T",
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# RMHD
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"mhd": "T",
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"relativity": "T",
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"Bx0": 0.5,
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# Patch 1 Left
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"patch_icpp(1)%geometry": 1,
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"patch_icpp(1)%x_centroid": 0.25,
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"patch_icpp(1)%length_x": 0.5,
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"patch_icpp(1)%vel(1)": 0.0,
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"patch_icpp(1)%vel(2)": 0.0,
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"patch_icpp(1)%vel(3)": 0.0,
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"patch_icpp(1)%pres": 1.0,
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"patch_icpp(1)%By": 1.0,
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"patch_icpp(1)%Bz": 0.0,
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"patch_icpp(1)%alpha_rho(1)": 1.0,
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"patch_icpp(1)%alpha(1)": 1.0,
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# Patch 2 Right
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"patch_icpp(2)%geometry": 1,
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"patch_icpp(2)%x_centroid": 0.75,
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"patch_icpp(2)%length_x": 0.5,
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"patch_icpp(2)%vel(1)": 0.0,
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"patch_icpp(2)%vel(2)": 0.0,
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"patch_icpp(2)%vel(3)": 0.0,
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"patch_icpp(2)%pres": 0.1,
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"patch_icpp(2)%By": -1.0,
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"patch_icpp(2)%Bz": 0.0,
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"patch_icpp(2)%alpha_rho(1)": 0.125,
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"patch_icpp(2)%alpha(1)": 1.0,
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# Fluids Physical Parameters
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"fluid_pp(1)%gamma": 1.0e00 / (2.0e00 - 1.0e00),
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"fluid_pp(1)%pi_inf": 0.0,
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}
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)
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)

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