A new Runge-Kutta discontinuous Galerkin method with conservation constraint to improve CFL condition for solving conservation laws

JOURNAL OF COMPUTATIONAL PHYSICS

卷:278

Article

Xu, Zhiliang¹  Chen, Xu-Yan²  Liu, Yingjie² 

[1] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Runge-Kutta discontinuous Galerkin method;    CFL condition;    Conservation laws;   

DOI  :  10.1016/j.jcp.2014.08.042

来源: Elsevier

【 摘 要 】

We present a new formulation of the Runge-Kutta discontinuous Galerkin (RKDG) method [5-8] for solving conservation laws with increased CFL numbers. The new formulation requires the computed RKDG solution in a cell to satisfy additional conservation constraint in adjacent cells and does not increase the complexity or change the compactness of the RKDG method. Numerical computations for solving one-dimensional and two-dimensional scalar and systems of nonlinear hyperbolic conservation laws are performed with approximate solutions represented by piecewise quadratic and cubic polynomials, respectively. The hierarchical reconstruction [16,32] is applied as a limiter to eliminate spurious oscillations in discontinuous solutions. From both numerical experiments and the analytic estimate of the CFL number of the newly formulated method, we find that: 1) this new formulation improves the CFL number over the original RKDG formulation by at least three times or more and thus reduces the overall computational cost; and 2) the new formulation essentially does not compromise the resolution of the numerical solutions of shock wave problems compared with ones computed by the RKDG method. (C) 2014 Published by Elsevier Inc.

【 授权许可】

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