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首页> 外文期刊>Journal of Computational Physics >The Elastoplast Discontinuous Galerkin (EDG) method for the Navier-Stokes equations
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The Elastoplast Discontinuous Galerkin (EDG) method for the Navier-Stokes equations

机译：Navier-Stokes方程的弹性不连续Galerkin（EDG）方法

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摘要

The present work details the Elastoplast (this name is a translation from the French " sparadrap", a concept first applied by Yves Morchoisne for Spectral methods [1]) Discontinuous Galerkin (EDG) method to solve the compressible Navier-Stokes equations. This method was first presented in 2009 at the ICOSAHOM congress with some Cartesian grid applications. We focus here on unstructured grid applications for which the EDG method seems very attractive. As in the Recovery method presented by van Leer and Nomura in 2005 for diffusion, jumps across element boundaries are locally eliminated by recovering the solution on an overlapping cell. In the case of Recovery, this cell is the union of the two neighboring cells and the Galerkin basis is twice as large as the basis used for one element. In our proposed method the solution is rebuilt through an L2 projection of the discontinuous interface solution on a small rectangular overlapping interface element, named Elastoplast, with an orthogonal basis of the same order as the one in the neighboring cells. Comparisons on 1D and 2D scalar diffusion problems in terms of accuracy and stability with other viscous DG schemes are first given. Then, 2D results on acoustic problems, vortex problems and boundary layer problems both on Cartesian or unstructured triangular grids illustrate stability, precision and versatility of this method.
机译：本工作详细介绍了弹性体（此名称是法文“ sparadrap”的译本，Yves Morchoisne首次将其应用于光谱方法[1]）;间断Galerkin（EDG）方法用于求解可压缩的Navier-Stokes方程。该方法于2009年在ICOSAHOM大会上首次使用笛卡尔网格应用程序提出。在此，我们将重点放在EDG方法似乎非常有吸引力的非结构化网格应用程序中。正如van Leer和Nomura在2005年提出的用于扩散的“恢复方法”一样，通过在重叠单元上恢复溶液可以局部消除跨元素边界的跳跃。在恢复的情况下，此单元格是两个相邻单元格的并集，并且Galerkin基础是用于一个元素的基础的两倍大。在我们提出的方法中，该解决方案是通过将不连续界面解决方案的L2投影重建在一个名为Elastoplast的小矩形重叠界面元素上的，该正交元素的阶数与相邻单元中的正交数相同。首先比较一维和二维标量扩散问题的准确性和稳定性，并与其他粘性DG方案进行比较。然后，关于笛卡尔或非结构三角网格上的声学问题，涡旋问题和边界层问题的二维结果说明了该方法的稳定性，准确性和多功能性。

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