Code | Basic characteristics |
Roe type-l
[107, 157, 59] |
Riemann solver of Roe type with arithmetic averaging; monotonicity preserving, linear reconstruction of primitive variables; 2nd order time stepping ([107, 157]: predictor-corrector; [59]: standard scheme) |
Roe-Eulderink
[49] |
Linearized Riemann solver based on Roe averaging; 2nd order accuracy in space and time |
HLL-l
[161] |
Harten-Lax-van Leer approximate Riemann solver; monotonic linear reconstruction of conserved / primitive variables; 2nd order accuracy in space and time |
LCA-phm
[106] |
Local linearization and decoupling of the system; PHM reconstruction of characteristic fluxes; 3rd order TVD preserving RK method for time stepping |
LCA-eno
[42] |
Local linearization and decoupling of the system; high order ENO reconstruction of characteristic split fluxes; high order TVD preserving RK methods for time stepping |
rPPM
[109] |
Exact (ideal gas) Riemann solver; PPM reconstruction of primitive variables; 2nd order accuracy in time by averaging states in the domain of dependence of zone interfaces |
Falle-Komissarov
[55] |
Approximate Riemann solver based on local linearizations of the RHD equations in primitive form; monotonic linear reconstruction of p, , and ; 2nd order predictor-corrector time stepping |
MFF-ppm
[111, 3] |
Marquina flux formula for numerical flux computation; PPM reconstruction of primitive variables; 2nd and 3rd order TVD preserving RK methods for time stepping |
MFF-eno/phm
[43] |
Marquina flux formula for numerical flux computation; upwind biased ENO/PHM reconstruction of characteristic fluxes; 2nd and 3rd order TVD preserving RK methods for time stepping |
MFF-l
[59] |
Marquina flux formula for numerical flux computation; monotonic linear reconstruction of primitive variables; standard 2nd order finite difference algorithms for time stepping |
Flux split
[59] |
TVD flux-split 2nd order method |
sTVD
[82] |
Davis (1984) symmetric TVD scheme with nonlinear numerical dissipation; 2nd order accuracy in space and time |
rGlimm
[187] |
Glimm's method applied to RHD equations in primitive form; 1st order accuracy in space and time |
rBS
[194] |
Relativistic beam scheme solving equilibrium limit of relativistic Boltzmann equation; distribution function approximated by discrete beams of particles reproducing appropriate moments; 1st and 2nd order TVD, 2nd and 3rd order ENO schemes |
Code | Basic characteristics |
Artificial viscosity | |
AV-mono
[28, 75, 113] |
Non-conservative formulation of the RHD equations (transport differencing, internal energy equation); artificial viscosity extra term in the momentum flux; monotonic 2nd order transport differencing; explicit time stepping |
cAV-implicit
[131] |
Non-conservative formulation of the RHD equations; internal energy equation; consistent formulation of artificial viscosity; adaptive mesh and implicit time stepping |
Flux corrected transport | |
FCT-lw
[45] |
Non-conservative formulation of the RHD equations (transport differencing, equation for ); explicit 2nd order Lax-Wendroff scheme with FCT algorithm |
SHASTA-c
[161, 39, 40] |
FCT algorithm based on SHASTA
[20]; advection of conserved variables |
van Putten's approach | |
van Putten
[181] |
Ideal RMHD equations in constraint-free, divergence form; evolution of integrated variational parts of conserved quantities; smoothing algorithm in numerical differentiation step; leap-frog method for time stepping |
Smooth particle hydrodynamics | |
SPH-AV-0
[102, 89] (SPH0) |
Specific internal energy equation; artificial viscosity extra terms in momentum and energy equations; 2nd order time stepping ([102]: predictor-corrector; [89]: RK method) |
SPH-AV-1
[102] (SPH1) |
Time derivatives in SPH equations include variations in smoothing length and mass per particle; Lorentz factor terms treated more consistently; otherwise same as SPH-AV-0 |
SPH-AV-c
[102] (SPH2) |
Total energy equation; otherwise same as SPH-AV-1 |
SPH-cAV-c
[164] |
RHD equations in conservation form; consistent formulation of artificial viscosity |
SPH-RS-c
[30] |
RHD equations in conservation form; dissipation terms constructed in analogy to terms in Riemann solver based methods |
Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller http://www.livingreviews.org/lrr-1999-3 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |