Artificial acoustic stiffness reduction in fully compressible, direct numerical simulation of combustion

A pseudo-compressibility method is proposed to modify the acoustic time step restriction found in fully compressible, explicit flow solvers. The method manipulates terms in the governing equations of orderMa2, whereMais a characteristic flow Mach number. A decrease in the speed of acoustic waves is obtained by adding an extra term in the balance equation for total energy. This term is proportional to flow dilatation and uses a decomposition of the dilatational field into an acoustic component and a component due to heat transfer. The present method is a variation of the pressure gradient scaling (PGS) method proposed in Ramshawet al(1985 Pressure gradient scaling method for fluid flowwith nearly uniform pressureJ. Comput. Phys.58 361–76). It achieves gains in computational efficiencies similar to PGS: at the cost of a slightly more involved right-hand-side computation, the numerical time step increases by a full order of magnitude. It also features the added benefit of preserving the hydrodynamic pressure field. The original and modified PGS methods are implemented into a parallel direct numerical simulation solver developed for applications to turbulent reacting flows with detailed chemical kinetics. The performance of the pseudo-compressibility methods is illustrated in a series of test problems ranging from isothermal sound propagation to laminar premixed flame problems.