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

作者：Xu Zhiliang^*; Chen Xu Yan; Liu Yingjie

来源：Journal of Computational Physics, 2014, 278: 348-377.

DOI：10.1016/j.jcp.2014.08.042

• Runge-Kutta discontinuous Galerkin method
• CFL condition
• Conservation laws

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.

• 出版日期2014-12-1