A Mach-uniform algorithm: Coupled versus segregated approach

A Mach-uniform algorithm is an algorithm with a good convergence rate for any level of the Mach number. In this paper, the severe time step restriction for low speed flows is removed by treating the acoustic and diffusive terms implicitly. After identification of these terms in the conservative set, we end up with a semi-implicit system. The way to solve this system can be chosen. Three different solution techniques are presented: a fully coupled algorithm, the coupled pressure and temperature correction algorithm [K. Nerinckx, J. Vierendeels, E. Dick, Mach-uniformity through the coupled pressure and temperature correction algorithm, Journal of Computational Physics 206 (2005) 597–623], and a fully segregated pressure-correction algorithm. We analyse the convergence behavior of the considered algorithms for some typical flow problems. Moreover, a Fourier stability analysis is done. For inviscid flow, the fully segregated and the fully coupled algorithm need about as much time steps to reach steady state. Therefore, the more segregation is introduced, the faster the calculation can be done. In case of heat transfer, the fully segregated pressure-correction algorithm suffers from a diffusive time step limit. This is not the case for the semi-segregated coupled pressure and temperature correction algorithm. Finally, when the gravity terms play an important role, only the fully coupled algorithm can avoid an additional time step restriction.