A low Mach number Euler formulation and application to timeiterative LBI schemes
Abstract
The Euler equations for a perfect gas are analyzed at low Mach numbers, and the results are applied to a timeiterative algorithm. The incompressible and compressible Euler equations are written in nondimensional vector form, and stagnationenthalpy terms are incorporated to derive nonsingular unsteady formulations which reduce to constantdensity incompressible expressions as the Mach number approaches zero. The constantenthalpy 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 steadysolution results to the split timeiterative linearizedblockinput algorithm of Briley and McDonald (1977). A significant improvement in convergence rate is demonstrated in a trial solution of the ensembleaveraged NavierStokes equations for turbulent flow in a 2D 90degbent channel.
 Publication:

AIAA Journal
 Pub Date:
 October 1983
 DOI:
 10.2514/3.8291
 Bibcode:
 1983AIAAJ..21.1467B
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Ideal Gas;
 Iterative Solution;
 Mach Number;
 Algorithms;
 Compressible Flow;
 Convergence;
 Incompressible Flow;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer