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The paper develops high-order accurate physical-constraints-preserving finitedifference 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 strongstability preserving time discretization. They are extensions of thepositivity-preserving finite difference WENO schemes for the non-relativisticEuler equations. However, developing physical-constraints-preserving methodsfor the RHD system becomes much more difficult than the non-relativistic casebecause of the strongly coupling between the RHD equations, no explicitexpressions of the primitive variables and the flux vectors, in terms of theconservative vector, and one more physical constraint for the fluid velocity inaddition to the positivity of the rest-mass density and the pressure. The keyis to prove the convexity and other properties of the admissible state set anddiscover a concave function with respect to the conservative vector replacingthe pressure which is an important ingredient to enforce thepositivity-preserving property for the non-relativistic case. Several one- andtwo-dimensional numerical examples are used to demonstrate accuracy,robustness, and effectiveness of the proposed physical-constraints-preservingschemes in solving RHD problems with large Lorentz factor, or strongdiscontinuities, or low rest-mass density or pressure etc.

High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics