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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations
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Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations

机译：浅水方程组的动态p自适应Runge-Kutta不连续Galerkin方法

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摘要

In this paper, dynamic p-adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for the two-dimensional shallow water equations (SWE) are investigated. The p-adaptive algorithm that is implemented dynamically adjusts the order of the elements of an unstructured triangular grid based on a simple measure of the local flow properties of the numerical solution. Time discretization is accomplished using optimal strong-stability-preserving (SSP) RK methods. The methods are tested on two idealized problems of coastal ocean modeling interest with complex bathymetry - namely, the idealization of a continental shelf break and a coastal inlet. Numerical results indicate the stability, robustness, and accuracy of the algorithm, and it is shown that the use of dynamic p-adaptive grids offers savings in CPU time relative to grids with elements of a fixed order p that use either local h-refinement or global p-refinement to adequately resolve the solution while offering comparable accuracy.
机译：本文研究了二维浅水方程（SWE）的动态p自适应Runge-Kutta不连续Galerkin（RKDG）方法。基于数值解的局部流动特性的简单度量，实现的p自适应算法动态调整非结构化三角网格的元素顺序。时间离散化是使用最佳的强稳定度（SSP）RK方法完成的。该方法针对复杂的测深法对沿海海洋建模感兴趣的两个理想问题进行了测试，即大陆架断裂和沿海入海口的理想化。数值结果表明了该算法的稳定性，鲁棒性和准确性，并且表明与使用局部h精炼或固定h阶的元素具有固定阶数p的网格相比，使用动态p自适应网格可以节省CPU时间。全局p优化可充分解决问题，同时提供可比的准确性。

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  • 作者

    Ethan J. Kubatko; Shintaro Bunya; Clint Dawson; Joannes J. Westerink;

  • 作者单位

    Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH 43210, United States;

    Department of Quantum Engineering and Systems Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-8656, Japan;

    Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX 78712, United States;

    Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, United States;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    discontinuous galerkin; adaptivity; shallow water equations;

    机译：不连续的隔间;适应性浅水方程;

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