论文标题
关于双曲线PDE的数值方法
On numerical methods for hyperbolic PDE with curl involutions
论文作者
论文摘要
在本文中，我们提出了三种不同的数值方法，以说明连续体物理学双曲线部分微分方程中的卷曲类型相关约束。所有方法都与Maxwell和MHD方程的现有和众所周知的发散方案有直接的类比。第一种方法包括对Godunov-Powell术语的概括，这意味着在PDE系统中添加适当的互动约束倍数，以实现对称的Godunov形式。第二种方法是Munz等人的广义Lagrangian乘数（GLM）方法的扩展，其中参与约束中的数值错误通过增强的PDE系统传播。最后的方法是保留离散化的准确相关性，类似于Maxwell和MHD方程的完全无差的方案，利用了适当交错的网格。我们提出了一些数值结果，可以将所有三种方法相互比较。
In this paper we present three different numerical approaches to account for curl-type involution constraints in hyperbolic partial differential equations for continuum physics. All approaches have a direct analogy to existing and well-known divergence-preserving schemes for the Maxwell and MHD equations. The first method consists in a generalization of the Godunov-Powell terms, which means adding suitable multiples of the involution constraints to the PDE system in order to achieve the symmetric Godunov form. The second method is an extension of the generalized Lagrangian multiplier (GLM) approach of Munz et al., where the numerical errors in the involution constraint are propagated away via an augmented PDE system. The last method is an exactly involution preserving discretization, similar to the exactly divergence-free schemes for the Maxwell and MHD equations, making use of appropriately staggered meshes. We present some numerical results that allow to compare all three approaches with each other.
