报告人：熊涛教授

报告题目：Asymptotic preserving and uniformly conditionally stable finite difference schemes for kinetic transport equations

报告摘要：

(1)In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic density, from the formal solution of the distribution function, which is then discretized by following characteristics for the transport part with a backward finite difference semi-Lagrangian approach, while the diffusive part is discretized implicitly. After the macroscopic density is available, the distribution function can be efficiently solved even with a fully implicit time discretization, since all discrete velocities are decoupled, resulting in a low-dimensional linear system from spatial discretizations at each discrete velocity. Both first and second order discretizations in space and in time are considered.

(2)The resulting schemes can be shown to be asymptotic preserving (AP) in the diffusive limit.  Uniformly unconditional stabilities are verified from a Fourier analysis based on eigenvalues of corresponding amplification matrices. Numerical experiments, including high dimensional problems, have demonstrated the corresponding orders of accuracy both in space and in time, uniform stability, AP property, and good performances of our proposed approach.

报告时间：2022.11.26  上午8:00-11:00

报告形式：腾讯会议；会议号：638-129-831

获取会议密码请发邮件至：yangchang@hit.edu.cn

报告人简介：熊涛，厦门大学数学科学学院教授，国家高层次青年人才。主要研究兴趣是计算流体力学和动理学方程的高精度数值方法。近年来发展了全马赫可压缩欧拉方程组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等杂志上。