Solution of the compressible flow equations

A technique is described for solving the compressible flow equations in subsonic flow. The general quasi‐linear equation ∇. g ∇ v = 0 is considered with g a function of ∇ v . ∇ v , and iterations of the form ∇. g n ∇ v n + 1 = 0 are analysed, where g 0 is suitably chosen and g n defined from v n for n ≥1. This approach is applied to the compressible flow equations in terms of a velocity potential ø: monotonic convergence is predicted and at each iteration the error is multiplied by a factor less than the square of the greatest Mach number in the solution. Reliable convergence has been obtained in practice solving the linear equation for ø n +1 by a finite difference method. The alternative of working in terms of the stream function ψ is discussed, and also discretization by the finite element method.