Riemann Solvers for Solving the Incompressible Navier-Stokes Equations Using theArtificial Compressibility Method

摘要

Five Riemann solvers for the artificial compressibility equations are presented.The mathematical character of the artificial compressibility equations is introduced. The exact and the two rarefaction Riemann solvers are presented. The local linearization solver, the Roe solver, and the HLLC (Harten-Leer-Lax Riemann where the C stands for contact) solver are included. Riemann solvers for the split two dimensional artificial compressibility equations are presented. The results of numerical tests performed on the various Riemann solvers and conclusions are given. These solvers give accurate results when used to produce global solutions to the test problem. The rarefaction solvers are computationally expensive, and offer no special advantage over the other solvers. The linear solver is the cheapest computationally, is simple and accurate to use in a program to find the solution to the Navier-Stokes equations. The HLLC solver is also relatively cheap, and very robust. Under certain conditions it may be better to select this solver above the linear one.