Computation of non-isothermal and compressible low Mach number gas flows by fully explicit scheme using control method for speed of sound

Abstract

In this study, we propose a new fully explicit scheme for non-isothermal and compressible low Mach number gas flows based on a fractional step method and a control method for the speed of sound. Since the Courant-Friedrichs-Lewy (CFL) condition based on the speed of sound is improved according to an artificial coefficient for pressure fluctuation terms, the time increment in the proposed method can be set on the same order as that of a conventional semi-implicit method which treats pressure terms in momentum and energy equations implicitly. As a result of the application to the natural convection in a square cavity, it is demonstrated that the proposed fully explicit method enables to conduct computations reasonably about 6 ～ 8 times faster than the conventional semi-implicit method by setting the appropriate value of the artificial coefficient for pressure fluctuation terms.