RKDG2 shallow-water solver on non-uniform grids with local time steps: Application to 1D and 2D hydrodynamics
RKDG2 shallow-water solver on non-uniform grids with local time steps: Application to 1D and 2D hydrodynamics
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DOI：
10.1016/j.apm.2014.08.009
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发表时间：
2015-02
影响因子：
5
通讯作者：
G. Kesserwani;Q. Liang
中科院分区：
文献类型：
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作者：
G. Kesserwani;Q. Liang
本文研究了带源项的非齐次浅水波方程的二阶Runge-Kutta间断Galerkin非一致解的局部时间推进方法。本文结合RKDG 2浅水流求解器（LTS-RKDG 2），重新考虑并改进了最近为齐次双曲型偏微分方程设计的LTS算法，包括地形和摩擦源项，以及湿润和干燥。两个LTS-RKDG 2计划，适应3和4级的LTS配置在1D和/或2D（四边形）的非均匀网格，分别采用3和4尺度的空间离散。选定的浅水基准测试用于验证，评估和比较LTS-RKDG 2方案相对于其传统的全球时间步长RKDG 2的替代品（GTS-RKDG 2），考虑到实际相关的水力建模的几个问题。结果表明，LTS-RKDG 2模型可以提供（取决于网格设置和流动的特征）与相关的GTS-RKDG 2模型相当的精度，在一维模拟中节省高达2.5倍的运行时间，在二维模拟中节省1.6倍的运行时间。
This paper investigates local time stepping (LTS) with the RKDG2 (second-order Runge–Kutta Discontinuous Galerkin) non-uniform solutions of the inhomogeneous SWEs (shallow water equations) with source terms. A LTS algorithm – recently designed for homogenous hyperbolic PDE(s) – is herein reconsidered and improved in combination with the RKDG2 shallow-flow solver (LTS-RKDG2) including topography and friction source terms as well as wetting and drying. Two LTS-RKDG2 schemes that adapt 3 and 4 levels of LTSs are configured on 1D and/or 2D (quadrilateral) non-uniform meshes that, respectively, adopt 3 and 4 scales of spatial discretization. Selected shallow water benchmark tests are used to verify, assess and compare the LTS-RKDG2 schemes relative to their conventional Global Time Step RKDG2 alternatives (GTS-RKDG2) considering several issues of practical relevance to hydraulic modelling. Results show that the LTS-RKDG2 models could offer (depending on both the mesh setting and the features of the flow) comparable accuracy to the associated GTS-RKDG2 models with a savings in runtime of up to a factor of 2.5 in 1D simulations and 1.6 in 2D simulations.