论文标题
约束保留不连续的Galerkin方法，用于在二维笛卡尔网格上理想可压缩的MHD
Constraint preserving discontinuous Galerkin method for ideal compressible MHD on 2-D Cartesian grids
论文作者
论文摘要
我们提出了一个约束，以在二维中和使用笛卡尔网格中自动维护无全局无差异属性的理想可压缩MHD的不连续的Galerkin方法。磁场的近似是使用raviart-thomas多项式实现的，而DG方案是基于这些多项式的某些矩的发展，从而自动保证无差异性能。我们还开发了HLL型多维Riemann求解器，以估计与1-D Riemann求解器一致的顶点的电场。当使用限制器时，无差异属性可能会丢失，并且通过无差重建步骤将其恢复。我们在一系列测试案例上显示了该方法的性能，最高准确性的第四顺序。
We propose a constraint preserving discontinuous Galerkin method for ideal compressible MHD in two dimensions and using Cartesian grids, which automatically maintains the global divergence-free property. The approximation of the magnetic field is achieved using Raviart-Thomas polynomials and the DG scheme is based on evolving certain moments of these polynomials which automatically guarantees divergence-free property. We also develop HLL-type multi-dimensional Riemann solvers to estimate the electric field at vertices which are consistent with the 1-D Riemann solvers. When limiters are used, the divergence-free property may be lost and it is recovered by a divergence-free reconstruction step. We show the performance of the method on a range of test cases up to fourth order of accuracy.
