Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

The paper proposes a second-order accurate finite volume local evolution Galerkin (FVLEG) method for two-dimensional special relativistic hydrodynamical (RHD) equations. Instead of using the dimensional splitting method or solving one-dimensional local Riemann problem in the direction normal to cell interface, the FVLEG method couples a finite volume formulation with the (genuinely) multi-dimensional approximate local evolution operator, which is derived by evolving the solutions of corresponding locally linearized RHD equations along all bicharacteristic directions. Several numerical examples are given to demonstrate the accuracy and the performance of the proposed FVLEG method.