Pressure gradient scaling method for fluid flow with nearly uniform pressure

Abstract

A method is described for increasing the efficiency of numerical calculations of compressible fluid flow problems in which the pressure field is nearly uniform in space. This condition is ordinarily satisfied at low Mach number. It is shown that in such problems, the pressure gradient in the momentum equation may be multiplied by a scaling factor 1 α 2 (α > 1) without significant effect, provided that α is not too large and that the pressure inhomogeneities are not of interest. This scaling modification reduces the acoustic speed by a factor of α, thereby increasing the effective Mach number by the same factor. This reduces the disparity between the acoustic and convective time scales, which improves the computational efficiency of many numerical schemes for compressible flow. The relation between the present approach and the α-transformation of O'Rourke and Bracco is briefly discussed. The practical utility of the method is illustrated by sample calculations of combustion in ideal gas mixtures.