A two-stage fourth-order discontinuous Galerkin method based on the GRP solver for the compressible euler equations

Abstract We develop a new fourth-order discontinuous Galerkin method using the generalized Riemann problem (GRP) solver based on the framework of the two-stage fourth-order accurate temporal discretization, with special application to compressible Euler equations. The appealing advantage of the two-stage fourth-order accurate temporal discretization is that it only takes a two-stage time-stepping to achieve the expected fourth-order accuracy. It turns out that the computational cost can be considerably reduced by more than 50% compared with the same order multi-stage SSP Runge–Kutta DG method. A number of test cases are presented to assess the accuracy and the efficiency of the two-stage fourth-order GRP-DG method, which demonstrates its appealing features to be an alternative approach for solving the unsteady compressible Euler equations.

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