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Code |
Basic characteristics |
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Artificial viscosity
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AV-mono [50 , 123 , 187 ] |
Non-conservative formulation of the RHD
equations |
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(transport differencing, internal
energy equation); |
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artificial viscosity extra term in the
momentum flux; |
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monotonic second-order transport
differencing; |
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explicit time stepping. |
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cAV-implicit [213 ] |
Non-conservative formulation of the RHD
equations; |
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internal energy equation; |
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consistent formulation of artificial
viscosity; |
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adaptive mesh and implicit time
stepping. |
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cAV-mono [10 ] |
Non-conservative formulation of the RHD
equations |
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(transport differencing, internal
energy equation); |
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consistent bulk scalar and tensorial
artificial viscosity; |
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monotonic second-order transport
differencing; |
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explicit time stepping. |
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Flux corrected transport
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FCT-lw [77 ] |
Non-conservative formulation of the RHD
equations |
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(transport differencing, equation for
); |
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explicit second-order Lax-Wendroff
scheme with FCT algorithm. |
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SHASTA-c |
FCT algorithm based on
SHASTA [33 ]; |
[256 , 69, 70 , 244 , 246 ] |
advection of conserved variables. |
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van Putten’s approach
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van Putten [287 ] |
Ideal RMHD equations in
constraint-free, divergence form; |
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evolution of integrated variational
parts of conserved quantities; |
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smoothing algorithm in numerical
differentiation step; |
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leap-frog method for time
stepping. |
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Smooth particle hydrodynamics
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SPH-AV-0 |
Specific internal energy equation; |
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[172 ] (SPH0), [150 ] |
artificial viscosity extra terms in
momentum and energy equations; |
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second-order time stepping |
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([172 ]:
predictor-corrector; [150 ]: RK method). |
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SPH-AV-1 [172 ] (SPH1) |
Time derivatives in SPH equations
include variations in smoothing |
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length and mass per particle; |
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Lorentz factor terms treated more
consistently; |
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otherwise same as SPH-AV-0. |
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SPH-AV-c [172 ] (SPH2) |
Total energy equation; |
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otherwise same as SPH-AV-1. |
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SPH-cAV-c [261 ] |
RHD equations in conservation
form; |
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consistent formulation of artificial
viscosity. |
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SPH-RS-c [53 ] |
RHD equations in conservation
form; |
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dissipation terms constructed in
analogy to terms in Riemann- |
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solver-based methods. |
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SPH-RS-gr [204 ] |
GR-SPH conservation
equations [202 ]; |
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dissipation terms as in [53 ]. |
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Table 5: |
Code
characteristics. |
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