Preconditioning and flux vector splitting for compressible low Mach number flow

Abstract

We tested five explicit methods to solve the quasi 1D Euler equations for compressible low Mach number flow through a Laval nozzle. All of them converge similarly slowly to the steady state, although at least the preconditioning methods and the semi-implicit flux vector splitting were expected to perform better. The reason is probably due to the use of reflecting boundary conditions. For low Mach number flow, the error in pressure of the flux vector splitting methods is lower than that of Roe's scheme.

Although about five times more costly per time step, the implicit Euler scheme with underrelaxation and proper implicit boundary treatment is about 100 times more efficient than the explicit Euler scheme, when applied to convection-pressure splitting or Roe's scheme even without preconditioning. Because of its accuracy and simplicity, we plan to test the convection-pressure splitting in 2D.