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首页> 外文期刊>Journal of Computational Physics >Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations
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Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations

机译：理想MHD方程的任意阶完全无散度的中心不连续Galerkin方法

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摘要

Ideal magnetohydrodynamic (MHD) equations consist of a set of nonlinear hyperbolic conservation laws, with a divergence-free constraint on the magnetic field. Neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions. In our recent work [F. Li, L. Xu, S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, Journal of Computational Physics 230 (2011) 4828-4847], second and third order exactly divergence-free central discontinuous Galerkin methods were proposed for ideal MHD equations. In this paper, we further develop such methods with higher order accuracy. The novelty here is that the well-established H(div)-conforming finite element spaces are used in the constrained transport type framework, and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence-free magnetic field. The overall algorithm is local, and it can be of arbitrary order of accuracy. Numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate.
机译：理想磁流体动力学（MHD）方程由一组非线性双曲守恒律组成，并且对磁场具有无散度约束。在计算方法的设计中忽略此约束可能导致数值不稳定或解决方案中的非物理特征。在我们最近的工作中[F. Li，L。Xu，S。Yakovlev，具有完全无散度磁场的理想MHD方程的中心不连续Galerkin方法，计算物理杂志230（2011）4828-4847]，二阶和三阶完全无散度的中心不连续提出了Galerkin方法用于理想的MHD方程。在本文中，我们将进一步开发具有更高阶精度的此类方法。这里的新颖之处在于，在受约束的输运类型框架中使用了完善的H（div）相容有限元空间，并且广泛探索了磁感应方程，以便提取足够的信息来唯一地重建完全无散度的磁。领域。整体算法是局部的，并且可以具有任意精度的顺序。数值算例表明了所提出方法的性能，特别是当它们是四阶精度时。

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