Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation

被引:8
作者
Beznosov, Oleksii [1 ]
Appelo, Daniel [2 ]
机构
[1] Univ New Mexico, Dept Math & Stat, 1 Univ New Mexico,MSC01 1115, Albuquerque, NM, Mexico
[2] Univ Colorado, Dept Appl Math, Univ Colorado 526 UCB, Boulder, CO 80309 USA
基金
美国国家科学基金会;
关键词
Wave equation; Overset grids; High order; Hermite methods; Discontinuous Galerkin methods; MAXWELLS EQUATIONS; UPWIND SCHEMES; ELEMENT-METHOD; PROPAGATION; DISCRETIZATION;
D O I
10.1007/s42967-020-00075-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present high order accurate numerical methods for the wave equation that combines efficient Hermite methods with geometrically flexible discontinuous Galerkin methods by using overset grids. Near boundaries we use thin boundary fitted curvilinear grids and in the volume we use Cartesian grids so that the computational complexity of the solvers approaches a structured Cartesian Hermite method. Unlike many other overset methods we do not need to add artificial dissipation but we find that the built-in dissipation of the Hermite and discontinuous Galerkin methods is sufficient to maintain the stability. By numerical experiments we demonstrate the stability, accuracy, efficiency, and the applicability of the methods to forward and inverse problems.
引用
收藏
页码:391 / 418
页数:28
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