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Numerical Solution of the Euler Equations with a Multiorder Discontinuous Finite Element Method

机译：多达不连续有限元法的欧拉方程的数值解

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摘要

Discontinuous Galerkin methods have proven to be very well suited for the construction of robust high order accurate numerical schemes on arbitrary unstructured and possibly non conforming grids for a wide variety of applications. These accurate, flexibile and robust methods are however rather expensive in terms of computational cost. In this paper we propose to address the issue of computational efficiency of discontinuous finite element methods by introducing a "multiorder" discontinuous Galerkin solution strategy which is similar to a multigrid techinque but uses progressively lower order polynomial DG approximations on the same grid instead of the same discretization on progressively coarsened grids. We present the results obtained in the numerical solution of the Euler equations for the subsonic flow around a circle which give some indication of the effectiveness ot the proposed multiorder solution strategy.
机译：不连续的Galerkin方法已经证明是非常适合于在各种应用的任意非结构化和可能的非符合网格上建造强大的高阶准确数字方案。然而，在计算成本方面，这些准确，柔韧性和鲁棒方法非常昂贵。在本文中，我们建议通过引入类似于MultiGrid Techinquque的“多达”不连续的Galerkin解决方案策略来解决不连续有限元方法的计算效率问题，但是在同一网格上使用逐渐下降的多项式DG近似而不是相同的在逐渐较粗糙的网格上的离散化。我们介绍了在圆圈围绕圆圈流动的euler方程的数值解中获得的结果，该圆圈提供了一些效果的指示，所提出的多功能解决方案策略。

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