一类通矢量分裂方法的保正性研究Ⅰ.显式格式  

ON POSITIVITY OF A CLASS OF FLUX-VECTOR SPLITTING METHODS I. EXPLICIT DIFFERENCE SCHEMES

作　　者：汤华中[1] 徐昆[2] 

机构地区：[1]北京大学数学科学学院,北京100871 [2]香港科技大学数学系

出　　处：《计算数学》2001年第4期469-476,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金(19901031);国家重点基础研究发展规划项目;计算物理国家级重点实验室基金;和科学与区程计算国家重点

摘　　要：This paper is about the positivity analysis of a class of flux-vector splitting (FVS) methods for the compressible Euler equations, which include gas-kinetic Beam scheme[8], Steger-Warming FVS method[9], and Lax-Friedrichs scheme. It shows that the density and the internal energy could keep non-negative values under the CFL condition for all above three schemes once the initial gas stays in a physically realizable state. The proof of positivity is closely related to the pseudo-particle representation of FVS schemes.This paper is about the positivity analysis of a class of flux-vector splitting (FVS) methods for the compressible Euler equations, which include gas-kinetic Beam scheme[8], Steger-Warming FVS method[9], and Lax-Friedrichs scheme. It shows that the density and the internal energy could keep non-negative values under the CFL condition for all above three schemes once the initial gas stays in a physically realizable state. The proof of positivity is closely related to the pseudo-particle representation of FVS schemes.

关 键 词：EULER方程 保正性 通矢量分裂 Beam格式 Lax-Friedrichs格式 通矢量方法 流体力学 数值方法 

分 类 号：O351[理学—流体力学] O241.8[理学—力学]