| Relativistic Hydrodynamics(RHD)is a branch of computational fluid dynamics theory that plays an important role in many subjects,including astrophysics and cosmology.With the development of numerical simulation methods,it plays an increasingly important role in the study of relativistic hydrodynamics.In recent years,some schemes related to entropy theory had developed for relativistic hydrodynamics equations,like entropy conservation scheme,entropy stability scheme,these have positive significance for the development of numerical schemes.In this paper,the construction methods of the two entropy schemes mentioned above were described,at the same time an entropy consistent scheme was proposed.Then a new slope limiter was obtained by using MUSCL data reconstruction,which can effectively improve the resolution and accuracy of entropy consistent scheme.Finally,several numerical experiments were tested to prove that entropy consistent scheme has good performance of the high-resolution.The main work of this paper was as follows:(1)An entropy consistent scheme for relativistic hydrodynamics equations was constructed.In this paper,the knowledge of hyperbolic conservation law equations was firstly introduced,and then the construction process of entropy schemes was described in detail.Since the relativistic hydrodynamics equations were closely related to the hyperbolic conservation laws equations,this numerical scheme was applied to the RHD equations,to obtain the entropy consistent numerical scheme for the relativistic hydrodynamics equations,and the convergence of entropy consistent scheme has proved,the phenomenon of non-physical can be effectively avoided.(2)A suitable slope limiter was introduced to construct a high-resolution entropy consistent scheme for RHD equations.By using MUSCL data reconstruction idea,the left and right values at the interface of cells were reconstructed,and a new slope limiter was obtained,so the high-resolution entropy consistent scheme of RHD equations was obtained.The convergence of this scheme has also proved.In this paper,the stability and robust properties of the new scheme were proved by numerical simulation of one-dimensional relativistic hydrodynamics equations.(3)The high-resolution entropy consistent scheme was extended to the two-dimensional.In this paper,we extended the high-resolution entropy consistent scheme of one-dimensional RHD equations to two-dimensional by method of dimension-by-dimension generalization,and the high-resolution entropy consistent scheme for two-dimensional RHD equations was obtained.Moreover by simulating several two-dimensional examples,the good characteristics of the new scheme were further demonstrated. |
