Generalized nonlinear boundary integral methods for compressible, viscous flows over arbitrary bodies: knowledge-based CFD

Abstract

Following a brief overview of the phenomenological and intuitive basis of the generalized boundary integral method, the paper outlines the mathematics which enable a physically realistic model of a compressible, rotational flow over an arbitrary body, including shock waves and vortical layers, to be reduced first to equivalent distributions of field source and vorticity, then to equivalent boundary distributions, and finally to a modification of the boundary conditions for a pseudo-Laplacian flow. A technique is proposed for splitting the field into an outer, inviscid zone in which the Euler equations are to be solved, and an inner, viscous zone in which the Navier-Stokes or compressible boundary-layer equations are required. The theory is applied to simple viscous/inviscid coupling, and shows that the popular ‘surface blowing’ model is deficient near an airfoil trailing edge; corrections are developed for the normal-velocity boundary condition and the resulting tangential velocity of the equivalent ‘inviscid’ problem.