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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws
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Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws

机译：具有双曲守恒律的具有时间精确本地时间步进的任意Lagrangian-Eulerian ADER-WENO有限体积方案

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摘要

In this article a new high order accurate cell-centered Arbitrary-Lagrangian-Eulerian (ALE) Godunov-type finite volume method with time-accurate local time stepping (LTS) is presented. The method is by construction locally and globally conservative. The scheme is based on a one-step predictor-corrector methodology in space-time and uses three main building blocks: First, a high order piecewise polynomial WENO reconstruction, to obtain a high order data representation in space from the known cell averages of the underlying finite volume scheme. Second, a high order space-time Galerkin predictor step based on a weak formulation of the governing PDE on moving control volumes. Third, a high order one-step finite volume scheme, based directly on the integral formulation of the conservation law in space-time. The algorithm being entirely based on space-time control volumes naturally allows for hanging nodes also in time, hence in this framework the implementation of a consistent and conservative time-accurate LTS becomes very natural and simple. The method is validated on some classical shock tube problems for the Euler equations of compressible gas dynamics and the magnetohydrodynamics equations (MHD). The performance of the new scheme is compared with a classical high order ALE finite volume scheme based on global time stepping. To the knowledge of the author, this is the first high order accurate Lagrangian finite volume method ever presented together with a conservative and time-accurate local time stepping feature.
机译：在本文中，提出了一种新的具有时间精确局部时间步长（LTS）的高阶精确细胞中心任意拉格朗日-欧拉（ALE）Godunov型有限体积方法。该方法是在本地和全球范围内构建的。该方案基于时空上的一步预测器-校正器方法，并使用三个主要构建块：首先，高阶分段多项式WENO重构，以从已知的单元平均获得空间中的高阶数据表示。基本的有限体积方案。其次，基于控制PDE在移动控制量上的弱公式，采用高阶时空Galerkin预测值步骤。第三，直接基于时空守恒律的积分公式的高阶单步有限体积方案。该算法完全基于时空控制量，自然也可以在时间上悬挂节点，因此，在此框架中，一致且保守的时间精确LTS的实现变得非常自然和简单。该方法在一些经典的冲击管问题上针对可压缩气体动力学的欧拉方程和磁流体动力学方程（MHD）进行了验证。将新方案的性能与基于全局时间步长的经典高阶ALE有限体积方案进行了比较。据作者所知，这是有史以来第一个高精确度的拉格朗日有限体积方法，同时具有保守且时间精确的本地时间步进功能。

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