Convergence acceleration for computing steady-state compressible flow at low Mach numbers

Abstract

A novel technique is introduced to accelerate the convergence of compressible low Mach number flow computations to the steady state. The stiffness due to the large disparity of flow velocity and acoustic wave speeds is bypassed by artificially reducing the speed of sound and thereby increasing the Mach number. This Mach number transformation is achieved by subtracting a constant value from the pressure in the entire flow field. Only the inviscid terms of the energy equation are influenced by that pressure decrease. The steady-state error is corrected by solving a scalar equation after each time step such that the steady-state solutions of the modified and non-modified schemes coincide. Thus, for each low Mach number simulation, one can obtain a convergence performance comparable to the corresponding simulation with a Mach number of about 0.4. This convergence acceleration is demonstrated for premixed laminar flames. If the present technique is implemented without time splitting, it corresponds to a novel low Mach number preconditioning.