New approaches for computation of low Mach number flows

Abstract

By using all speed numerical flux schemes, such as SLAU [Simple Low Dissipation AUSM (Advection Upstream Splitting Method)], in MUSCL (Monotone Upwind Scheme for Conservation Laws) approach for compressible CFD, low Mach number flows can be computed without loss of accuracy nor parameter tuning. For an efficient computation, this paper deals with new approaches of implicit time integration method. In this approach, the large sparse matrix system, which consists of flux Jacobian of numerical flux function, has to be solved in each time step. Firstly, a simple Gauss–Seidel iteration method named TC-PGS1(Time Consistent Preconditioned Gauss–Seidel 1) which has flavor of the time derivative preconditioning is introduced. Secondary, we tried to use FGMRES (k) (Flexible Generalized Minimum Residual Method) to solve the non-diagonal dominant linear system arising from Jacobian of flux function SLAU. TC-PGS1 is also used as the matrix preconditioner for FGMRES (k). Optimal parameters for FGMRES (k) is investigated numerically and the performances on computational efficiency of the new methods are compared. It is indicated that FGMRES (k) has apparent advantage on computation of low Mach number flows with sound propagation, however, simpler TC-PGS1 has comparable performance if only flow fields are of interest.