An eigenvector-based linear reconstruction approach for time stepping in discontinuous Galerkin scheme used to solve shallow water equations

作者：Araud Quentin^*; Finaud Guyot Pascal; Guinot Vincent; Mose Robert; Vazquez Jose

来源：International Journal for Numerical Methods in Fluids, 2012, 70(12): 1590-1604.

DOI：10.1002/fld.3645

• EVR method
• second-order time stepping
• discontinuous Galerkin technique
• shallow water equations

Discontinuous Galerkin (DG) methods have shown promising results for solving the two-dimensional shallow water equations. In this paper, the classical RungeKutta (RK) time discretisation is replaced by the eigenvector-based reconstruction (EVR) that allows the second-order time accuracy to be achieved within a single time-stepping procedure. Moreover, the EVRDG approach yields stable solutions near drying and wetting fronts, whereas the classical RKDG approach yields instabilities. The proposed EVRDG technique is compared with the original RKDG approach on various test cases with analytical solutions. The EVRDG solutions are shown to be as accurate as those obtained with the RKDG scheme. Besides, the EVRDG scheme is 1.6 times faster than the RKDG method. Simulating dambreaks involving dry beds confirms that EVRDG scheme gives correct solutions, whereas the RKDG method yields instabilities.

• 出版日期2012-12-30