Hao Li
Purdue University
Title
A fourth order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations
Abstract
We demonstrate that the classical fourth order accurate compact finite difference scheme satisfies a natural weak monotonicity property for solving scalar convection-diffusion equations. Based on such a property, we design a simple limiter to enforce the bound-preserving or positivity-preserving property of numerical solutions without losing conservation or high order accuracy. Higher order schemes including 6th and 8th order schemes satisfying the weak monotonicity can also be constructed. We show that the bound-preserving property is still valid when a total-variation-bounded (TVB) limiter is used to reduce oscillations. All these results can be easily extended to higher dimensions and passive convection such as incompressible flows. More general boundary conditions such as the inflow-outflow boundary condition will also be discussed. This is a joint work with Prof. Shusen Xie at Ocean University of China and Prof. Xiangxiong Zhang at Purdue University.
Date
14:30-15:30, December 18th, 2017
Conference Room
Room 606 at School of Mathematical Sciences