Evaluation of Inviscid Fluxes

For the Coupled Flow model, Simcenter STAR-CCM+ provides two schemes for evaluating inviscid fluxes—the Weiss-Smith Preconditioned Roe's Flux-Difference Splitting (ROE FDS) scheme and Liou's AUSM+ Flux-Vector Splitting (AUSM+ FVS) scheme.

Like the ROE FDS scheme ([293], [294]), the AUSM+ FVS scheme ([189], [190]) is based on the upwind concept, which is applied consistently on the two physically distinct parts of the inviscid flux: convective and pressure. The AUSM+ inviscid flux scheme is the more appropriate choice for solving flows involving high supersonic and/or hypersonic regimes (Mach number of around 3 and above), when compared with the Roe scheme.

The main advantages of the AUSM+ scheme are:

  • Algorithmic simplicity and straightforward extension for complex conservation laws.
  • Accurate capture of shock- and contact-discontinuity.
  • Numerical solutions that preserve positivity and satisfy entropy.
  • Reduced susceptibility to “carbuncle” phenomena.

AUSM+-up is the low-Mach preconditioned formulation that is used in Simcenter STAR-CCM+. It is included primarily as an option for use with high supersonic and/or hypersonic flows. It also provides uniform accuracy and robust convergence for all Mach number flows.

The AUSM+-up scheme can be employed for solving a wide range of flow problems including incompressible to hypersonic aerodynamics, turbomachinery flows, LES/DES of turbulent flows and aeroacoustics.