Inverse Lax-Wendroff Procedure for Numerical Boundary Conditions

题目:Inverse Lax-Wendroff Procedure for Numerical Boundary Conditions





Abstract:We discuss a recent development of a high order finite difference numerical boundary condition for solving hyperbolic Hamilton-Jacobi equations, hyperbolic conservation laws, and convection-diffusion equations on complex geometry using a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary may not be aligned with the mesh. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions coupled with traditional extrapolation or weighted essentially non-oscillatory (WENO) extrapolation for outflow boundary conditions. The schemes are shown to be high order and stable, under the standard CFL condition for the inner schemes, regardless of the distance of the first grid point to the physical boundary, that is, the “cut-cell” difficulty is overcome by this procedure. Numerical examples are provided to illustrate the good performance of our method.  This is a joint work with Jinwei Fang, Ling Huang, Tingting Li, Jianfang Lu, Jianguo Ning, Sirui Tan,

Francois Vilar, Cheng Wang and Mengping Zhang.

舒其望教授简介:舒其望,美国布朗大学教授,应用数学系主任,中国科技大学”长江学者奖励计划”讲座教授。美国数学会理事会成员,美国数学学会杂志”Mathematics of Computation”主编,美国Springer杂志”Journal of Scientific Computing”主编以及十余种国际计算和应用数学杂志的编委。主要研究兴趣包括计算流体力学和偏微分方程数值解,在国际一流杂志发表论文140余篇,论文被同行广泛引用。曾获美国宇航和太空总署计算流体力学成就奖和中科院冯康科学计算奖。2012年11月1日,入选美国数学学会(American Mathematical Society,简称AMS)首届会士名单。