THE LEAST-SQUARES FINITE-ELEMENT METHOD FOR LOW-MACH-NUMBER COMPRESSIBLE VISCOUS FLOWS

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible hows pose as an extreme. The conventional approach requires special treatments for low-speed hows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique, and finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such a difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: driven cavity flows at various Reynolds numbers and buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.