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A bound-preserving high order scheme for variable density incompressible Navier-Stokes equations

Abstract

For numerical schemes to the incompressible Navier-Stokes equations with variable density, it is a critical property to preserve the bounds of density. A bound-preserving high order accurate scheme can be constructed by using high order discontinuous Galerkin (DG) methods or finite volume methods with a bound-preserving limiter for the density evolution equation, with any popular numerical method for the momentum evolution. In this talk, we consider a combination of a continuous finite element method for momentum evolution and a bound-preserving DG method for density evolution. Fully explicit and explicit-implicit strong stability preserving Runge-Kutta methods can be used for the time discretization for the sake of bound-preserving. Numerical tests on representative examples are shown to demonstrate the performance of the proposed scheme.


Short bio

李茂军,电子科技大学副教授,博士生导师。2006年本科毕业于重庆大学,2012年12月在重庆大学获理学博士学位。2011年8月到2012年8月在美国伦斯勒理工学院访问。2013年2月到2014年8月在北京计算科学研究中心从事博士后研究。目前主要从事浅水波问题、两相流问题,磁流体问题等流体力学问题的数值方法研究。主持国家自然科学基金青年项目1项,面上项目1项,第一主研参与国家自然科学基金重点项目1项。迄今为止在Journal of Computational Physics,SIAM Journal on Scientific Computing,Journal of Scientific Computing,Communications in Computational Physics,Journal of Computational and Applied Mathematics, Applied Numerical Mathematics等期刊上发表SCI学术论文近20篇。