A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations
A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations
复制标题
非线性守恒定律的可扩展指数 DG 方法：应用于 Burger 和 Euler 方程
DOI：
10.1016/j.cma.2021.114031
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发表时间：
2021
影响因子：
7.2
通讯作者：
Bui-Thanh, Tan
中科院分区：
文献类型：
--
作者：
Kang, Shinhoo;Bui-Thanh, Tan
We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics extracted by linearization) and nonlinear (the remaining after removing the former) parts, on which we apply the discontinuous Galerkin (DG) spatial discretization. The resulting semi-discrete system is then integrated using exponential time-integrators: exact for the former and approximate for the latter. By construction, our approach i) is stable with a large Courant number (C r> 1); ii) supports high-order solutions both in time and space; iii) is computationally favorable compared to IMEX DG methods with no preconditioner; iv) requires comparable computational time compared to explicit RKDG methods, while having time stepsizes orders magnitude larger than maximal stable time stepsizes for explicit RKDG methods; v) is scalable in a modern massively parallel computing architecture by exploiting Krylov-subspace matrix-free exponential time integrators and compact communication stencil of DG methods. Various numerical results for both Burgers and Euler equations are presented to showcase these expected properties. For Burgers equation, we present a detailed stability and convergence analyses for the exponential Euler DG scheme.
