无发散磁流体力学的rkdg和混合rkdg+hweno格式（I）
rkdg and Hybrid rkdg+hweno Schemes for Divergence-Free Magnetohydrodynamics Part I
摘要：
Balsara（2001）指出了无发散重构在磁流体动力学（MHD）自适应网格细化问题中的重要性，Balsara（2004）也指出了无发散重构对于设计MHD鲁棒二阶格式的重要性。在本文中，我们表明，重建的发散自由向量场可以进行优于二阶精度。因此，我们设计了无发散的RKDG和混合RKDG+HWENO格式的MHD，具有优于二阶的精度。精度分析表明，对于光滑问题，格式满足设计精度。严格的一维测试也表明，这些测试的计划表现良好。
英文摘要：
Balsara (2001) showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics (MHD) and the importance of the same for designing robust second order schemes for MHD was shown in Balsara (2004). In this paper we show that the reconstruction of divergence-free vector fields can be carried out with better than second order accuracy. As a result, we design divergence-free RKDG and hybrid RKDG+HWENO schemes for MHD that have accuracies that are better than second order. Accuracy analysis is carried out and it is shown that the schemes meet their design accuracy for smooth problems. Stringent one-dimensional tests are also presented showing that the schemes perform well on those tests.
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