HPC Tier Module
Ideal MHD (HLLD Riemann)
Ideal MHD with the HLLD five-wave solver, leading with the honest HLLD-vs-HLL comparison.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Comparing Riemann solvers for magnetohydrodynamics fairly - showing where the extra waves actually matter - is fiddly to set up outside a full astrophysics code.
The local-first solution
This plugin drives the real wasm MHD engine in the browser with the Miyoshi-Kusano HLLD five-wave solver run alongside HLL, leading with the honest comparison where HLLD restores the contact and Alfven waves HLL averages over.
What it does
1D ideal MHD with HLLD, MUSCL reconstruction, RK3-TVD time stepping
HLL run alongside for a direct HLLD-vs-HLL diffusivity comparison
Exact circularly polarized Alfven wave: true L1 error of By vs the translated profile
Brio-Wu shock tube benchmarked against a self-converged HLLD reference
Mass and energy conserved with div B identically zero (Bx constant in 1D)
Honest scope
This is classical (non-relativistic) ideal MHD in 1D; the 2D/3D div-B problem and constrained transport are a separate concern handled elsewhere. A bridge to HPC, not a replacement for Athena++, PLUTO, or FLASH, and EXACT is never asserted for a discretized finite-volume solution. The engine's own GeoNum verdict is passed through unchanged.
Authorities cited
- Miyoshi, T. & Kusano, K. (2005). A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics. J. Comput. Phys. 208, 315-344. DOI 10.1016/j.jcp.2005.02.017.
- Brio, M. & Wu, C. C. (1988). An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 75, 400-422. DOI 10.1016/0021-9991(88)90120-9.
- Toth, G. (2000). The div B = 0 constraint in shock-capturing MHD codes. J. Comput. Phys. 161, 605-652. (Circularly polarized Alfven wave as an exact nonlinear test.)
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Compare HLLD vs HLL
Run the solver in the browser and save the comparison to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing leaves your machine to anyone's cloud.