A low Mach number Euler formulation and application to time-iterative LBI schemes

The Euler equations for a perfect gas are analyzed at low Mach numbers, and the results are applied to a time-iterative algorithm. The incompressible and compressible Euler equations are written in nondimensional vector form, and stagnation-enthalpy terms are incorporated to derive nonsingular unsteady formulations which reduce to constant-density incompressible expressions as the Mach number approaches zero. The constant-enthalpy state is shown to be a good approximation for inviscid adiabatic flows, subsonic or transonic viscous flows with Prandtl number = 1 and no heat addition, and incompressible flows with a Mach number set at a small (e.g., less than 0.1) value. A diagonal conditioning matrix is developed to apply the steady-solution results to the split time-iterative linearized-block-input algorithm of Briley and McDonald (1977). A significant improvement in convergence rate is demonstrated in a trial solution of the ensemble-averaged Navier-Stokes equations for turbulent flow in a 2D 90-deg-bent channel.