论文标题
MHD方程和熵原理的整体抛物线正则化
Monolithic parabolic regularization of the MHD equations and entropy principles
论文作者
论文摘要
我们在PDE级别表明，理想磁流失动力学方程（MHD）的整体抛物线正则化与所有通用熵兼容，可满足最低熵原理，并保留密度和内部能量的阳性。然后，我们使用空间中的连续有限元元素进行数值研究对MHD方程的正则化，并及时明确保留了强大的稳定性。正规化项的人工粘度系数与MHD的熵残差成正比。结果表明，该方法具有很高的准确性，可用于平滑问题，并准确地捕获强烈的冲击和不平滑问题的不连续性。
We show at the PDE level that the monolithic parabolic regularization of the equations of ideal magnetohydrodynamics (MHD) is compatible with all the generalized entropies, fulfills the minimum entropy principle, and preserves the positivity of density and internal energy. We then numerically investigate this regularization for the MHD equations using continuous finite elements in space and explicit strong stability preserving Runge-Kuta methods in time. The artificial viscosity coefficient of the regularization term is constructed to be proportional to the entropy residual of MHD. It is shown that the method has a high order of accuracy for smooth problems and captures strong shocks and discontinuities accurately for non-smooth problems.
