Implementation of Finite Difference Weighted Compact Nonlinear Schemes with the Two-Stage Fourth-Order Accurate Temporal Discretization

Authors

  • Zhiwei He Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China.
  • Fujie Gao Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China.
  • Baolin Tian Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, China.
  • Jiequan Li Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China and Center for Applied Physics and Technology, Peking University, Beijing 100871, China

DOI:

https://doi.org/10.4208/cicp.OA-2019-0029

Keywords:

Hyperbolic conservation laws, finite difference method, Lax-Wendroff type time discretization, WCNS.

Abstract

In this paper, we present a new two-stage fourth-order finite difference weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws with special application to compressible Euler equations. To construct this algorithm, apart from the traditional WCNS for the spatial derivative, it was necessary to first construct a linear compact/explicit scheme utilizing time derivative of flux at midpoints, which, in turn, was solved by a generalized Riemann solver. Combining these two schemes, the fourth-order time accuracy was achieved using only the two-stage time-stepping technique. The final algorithm was numerically tested for various one-dimensional and two-dimensional cases. The results demonstrated that the proposed algorithm had an essentially similar performance as that based on the fourth-order Runge-Kutta method, while it required 25 percent less computational cost for one-dimensional cases, which is expected to decline further for multidimensional cases.

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Published

2020-05-06

Issue

Vol. 27 No. 5 (2020)

Section

Articles