High order asymptotic preserving finite difference schemes with constrained transport for MHD equations in all sonic Mach numbers
报告题目: High order asymptotic preserving finite difference schemes with constrained transport for MHD equations in all sonic Mach numbers
报告专家：熊涛 教授（厦门大学）
报告时间：2022年12月14日 10:00—11:00
报告形式：腾讯会议ID：276-446-063，
报告摘要:In this work, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence free finite difference weighted essentially non-oscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number ε ranging from 0 to O(1). High-order accuracy in time is obtained by SI implicit-explicit Runge-Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.
专家简介：熊涛，厦门大学数学科学学院教授，国家高层次青年人才，主要从事计算流体力学和动理学方程高精度数值算法的研究，近年来发展了全马赫可压缩欧拉方程组等跨流域问题的一致稳定渐近保持有限差分WENO方法，多尺度动理学方程的一致稳定渐近保持间断Galerkin有限元方法等，部分成果发表在SIAM Journal on Scientific Computing和Journal of Computational Physics等杂志。
邀请人：贺巧琳