NIMS 집중강연: Lectures on Numerical Methods for Hyperbolic Conservation Laws

07/19/2016 - 07/20/2016
NIMS 집중 강연 연사 : James A. Rossmanith (Iowa State University) 일시 : 2016년 7월 19일~20일 오후 4시~6시 장소 : 국가수리과학연구소 CAMP 대형세미나실 Title : Lectures on Numerical Methods for Hyperbolic Conservation Laws Abstract: Hyperbolic conservation laws arise as model equations in a variety of different applications. The key defining characteristic of hyperbolic conservation laws are the finite propagation of information. Some examples of applications include traffic flow, porous media flow, tsunami modeling, compressible gas dynamics, plasma physics, and general relativity. In these four lectures I will introduce the idea of hyperbolic conservation laws, explain the paradigm of finite volume methods (FVM), explain the discontinuous Galerkin finite element method (DG-FEM), and discuss issues related to non-oscillatory and positivity-preserving limiters. At the end I will describe some recent and ongoing work on the Lax-Wendroff DG-FEM and its associated limiters. Lecture 1: Hyperbolic conservation laws, finite volume methods, and the Godunov scheme Lecture 2: Approximate Riemann solvers and relaxation schemes Lecture 3: Discontinuous Galerkin finite element methods (DG-FEM) and limiters Lecture 4: Lax-Wendroff DG-FEM and a new positivity limiter