Matching Procedure for Viscous-Inviscid Interactive Calculations x

Abstract

Introduction 7N this Note, we describe a procedure for coupling a viscous Jl boundary-layer calculation with a solution of the Euler equations. The interaction between the viscous calculation and the rotational inviscid calculation is accomplished by means of an iterative process. An iterative approach to the subsonic interaction problem is not uncommon; several researchers have used this approach in conjunction with the displacement thickness concept to obtain better approximations to flows (e.g., Refs. 2 and 3). However, the present interactive method differs from these procedures in two ways. First, the present method does not rely solely on the mechanism of a physical displacement of the outer flow streamlines by the viscous layer to achieve coupling of the viscous and inviscid calculations. The interaction takes the form of an injection at solid surfaces, but it is different from the usual equivalent source distribution technique in that this injection has a momentum and enthalpy character. Second, the viscous solution is constructed in a manner suggested by the theory of matched asymptotic expansions. In order to illustrate the operation of this procedure more clearly, we discuss the specific case where the inviscid solution is an explicit time-marching, finite-difference calculation (e.g., MacCormack's method). However, the applicability of the method is not restricted to this choice.