an:06660724
Zbl 1349.76550
Wu, Kailiang; Tang, Huazhong
High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
EN
J. Comput. Phys. 298, 539-564 (2015).
0021-9991
2015
j
76M20 65M06 76L05 76V05 76Y05 80A32
finite difference scheme; physical-constraints-preserving; high-order accuracy; weighted essentially non-oscillatory; relativistic hydrodynamics; Lorentz factor
Summary: The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrichs 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 formulas of the primitive variables and the flux vectors with respect to 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 instead of 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.