A two-stage fourth-order discontinuous Galerkin method based on the GRP solver for the compressible euler equations. (15th March 2019)

• Record Type: Journal Article
• Authors: Cheng, Jian; Du, Zhifang; Lei, Xin; Wang, Yue; Li, Jiequan
• Is Part Of: Computers & fluids. Volume 181(2019)
• Page Start: 248
• Page End: 258
• Publication Date: 2019-03-15
• Subjects: Discontinuous Galerkin method -- Two-stage fourth-order accurate scheme -- GRP Solver -- The euler equations; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2019.01.025
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: A new two-stage fourth-order discontinuous Galerkin method is developed. Generalized Riemann problem is solved at each cell interface. Computational cost can be considerably reduced compared to using multi-stage TVD Runge–Kutta method. 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.