11,432 research outputs found
Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations
This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook)
schemes in the framework of finite volume method for the ultra-relativistic
flows. Different from the existing kinetic flux-vector splitting (KFVS) or
BGK-type schemes for the ultra-relativistic Euler equations, the present
genuine BGK schemes are derived from the analytical solution of the
Anderson-Witting model, which is given for the first time and includes the
"genuine" particle collisions in the gas transport process. The BGK schemes for
the ultra-relativistic viscous flows are also developed and two examples of
ultra-relativistic viscous flow are designed. Several 1D and 2D numerical
experiments are conducted to demonstrate that the proposed BGK schemes not only
are accurate and stable in simulating ultra-relativistic inviscid and viscous
flows, but also have higher resolution at the contact discontinuity than the
KFVS or BGK-type schemes.Comment: 41 pages, 13 figure
High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
The paper develops high-order accurate physical-constraints-preserving finite
difference WENO schemes for special relativistic hydrodynamical (RHD)
equations, built on the local Lax-Friedrich splitting, the WENO reconstruction,
the physical-constraints-preserving flux limiter, and the high-order strong
stability preserving time discretization. They are extensions of the
positivity-preserving finite difference WENO schemes for the non-relativistic
Euler equations. However, developing physical-constraints-preserving methods
for the RHD system becomes much more difficult than the non-relativistic case
because of the strongly coupling between the RHD equations, no explicit
expressions of the primitive variables and the flux vectors, in terms of the
conservative vector, and one more physical constraint for the fluid velocity in
addition to the positivity of the rest-mass density and the pressure. The key
is to prove the convexity and other properties of the admissible state set and
discover a concave function with respect to the conservative vector replacing
the pressure which is an important ingredient to enforce the
positivity-preserving property for the non-relativistic case. Several one- and
two-dimensional numerical examples are used to demonstrate accuracy,
robustness, and effectiveness of the proposed physical-constraints-preserving
schemes in solving RHD problems with large Lorentz factor, or strong
discontinuities, or low rest-mass density or pressure etc.Comment: 39 pages, 13 figure
Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic
fluids recently proposed in Ref. [1], is presented. The method is numerically
validated and applied to the case of two quite different relativistic fluid
dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the
impact of a supernova blast-wave on massive interstellar clouds. Close to
second order convergence with the grid resolution, as well as linear dependence
of computational time on the number of grid points and time-steps, are
reported
Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement
Astrophysical relativistic flow problems require high resolution
three-dimensional numerical simulations. In this paper, we describe a new
parallel three-dimensional code for simulations of special relativistic
hydrodynamics (SRHD) using both spatially and temporally structured adaptive
mesh refinement (AMR). We used the method of lines to discretize the SRHD
equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme
for time integration. For spatial reconstruction, we have implemented piecewise
linear method (PLM), piecewise parabolic method (PPM), third order convex
essentially non-oscillatory (CENO) and third and fifth order weighted
essentially non-oscillatory (WENO) schemes. Flux is computed using either
direct flux reconstruction or approximate Riemann solvers including HLL,
modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR
part of the code is built on top of the cosmological Eulerian AMR code {\sl
enzo}. We discuss the coupling of the AMR framework with the relativistic
solvers. Via various test problems, we emphasize the importance of resolution
studies in relativistic flow simulations because extremely high resolution is
required especially when shear flows are present in the problem. We also
present the results of two 3d simulations of astrophysical jets: AGN jets and
GRB jets. Resolution study of those two cases further highlights the need of
high resolutions to calculate accurately relativistic flow problems.Comment: 14 pages, 23 figures. A section on 3D GRB jet simulation added.
Accepted by ApJ
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