Schemes of Roe, HLL, HLLC, Burgers; Equations of 1D, 2D, 3D; Euler, SRHD, Maxwell, Bona-Masso ADM; Implemented in OpenCL
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OpenCL Riemann solver for computational fluid dynamics.

A finite volume solver based on hyperbolic formalisms.

Works in 1D, 2D, and 3D.

Simulates Euler equations, SRHD, Maxwell, and ADM formalism (Bona-Masso) numerical relativity. Almost got MHD working.

Euler is simulated via Burgers, HLL, HLLC, Roe.

SRHD via Roe.

Maxwell via Roe.

ADM Bona-Masso via Roe.

MHD, I'm working on a Burgers, HLLC, and Roe ... though none are working yet.

Slope limiters are working on all Burgers and Roe solvers.

Support for Periodic, Mirror, and Free-Flow boundary methods.

Self-gravity option for Euler and MHD equation solvers.

Might get around to CG or GMRes method of Backward Euler implicit integration.

Bona-Masso ADM Numerical Relativity Results:

gravitational wave extrinsic curvature:

gravitational wave extrinsic curvature

slow and stable warp bubble

slow and stable warp bubble

alcubierre warp bubble collapse

alcubierre warp bubble collapse








  • Trangenstein "Numerical Simulation of Hyperbolic Conservation Laws"

Numerical Relativity- ADM, BSSN, etc:

  • Alcubierre, Miguel. Introduction to 3+1 Numerical Relativity. Oxford Science Publications, Oxford, 2008.
  • Baumgarte, Shapiro. Numerical Relativity: Solving Einstein's Equations on the Computer, 2010.

Stellar Schwarzschild initial conditions:

  • Misner, Thorne, Wheeler. Gravitation, 1973


  • Marti, J. M. and Muller, E. Numerical Hydrodynamics in Special Relativity Living Reviews in Relativity 6 (2003), 7
  • Sheck, Aloy, Marti, Gomez, Muller Does the plasma composition affect the long-term evolution of relativistic jets? Monthly Notices of Royal Astronomical Society 331, 615-634 2002.
  • Anton, Luis; Zanotti, Olindo; Miralles, Juan; Marti, Jose; Ibanez, Jose; Font, Jose; Pons, Jose. Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach February 2, 2008


MHD Roe:

MHD initial conditions:

  • Brio, M. & C.C. Wu, "An Upwind Differencing Scheme for the Equations of Ideal Magnetohydrodynamics", Journal of Computational Physics, 75, 400-422 (1988). The test is described in Section V.

Runge Kutta & TVD RK: