Title：The positivity-preserving numerical method for compressible multi-media flow
Speaker：Wang, Chunwu (王春武 )
Affiliation：南京航空航天大学
Time：14:00 - 15:00, 9/4/2021
Venue：南京应用数学中心一楼报告厅
Inviter：刘继军教授（101008811@seu.edu.cn）
Abstract：In the numerical simulations of the multi-medium flow such as blast waves or high-velocity jets, the negative density or pressure (or internal energy) may occur in the low density and low pressure domain due to the numerical errors of the high order schemes. The loss of positivity of the physically positive variables may lead to nonlinear instability or blow-ups of the algorithm. In this paper, we present a positivity-preserving algorithm for the compressible multi-media flow. The real Ghost Fluid method (RGFM) is coupled to the positivity-preserving Runge-Kutta discontinuous Galerkin (RKDG) schemes for single medium flow to treat the interface. The two-shock approximate Riemann problems are used to produce the fluid states at the interface. To solve the Riemann problems at the interface in RGFM, an iteration method is constructed and proved to be able to give the positive solver of density and pressure if the initial data is positive. Several numerical examples are given to test robustness and efficiency of the algorithm. Numerical results show that the obtained method can maintain the positivity of density and pressure and capture the discontinuities accurately.
报告人介绍：王春武，南京航空航天大学教授，博士生导师，理学院院长。2000年南京航空航天大学流体力学专业获工学博士学位。曾多次赴美国布朗大学、新加坡高性能计算研究所等科研单位和院校开展合作研究。主要研究方向为偏微分方程数值解。已在J. Comput. Phy., SIAM J. Sci. Comput.等重要期刊上发表学术论文数十篇。主持完成国家自然科学基金项目、国防科研项目、国家重点实验室科研项目等十余项。
