Robust viscous-inviscid interaction scheme for application on unstructured meshes

Abstract

A coupled viscous-inviscid interaction scheme combining the continuity equation for potential flow with the three-dimensional integral boundary layer equations is presented. The inviscid problem is discretized by a finite-element approach whereas an upwind-biased finite-volume scheme is employed for the boundary layer equations. The discretization is applicable to unstructured tetrahedral-triangular meshes and results in a sparse system of non-linear equations which is solved by a Newton-type method. The mathematical reasons for the singularities commonly associated with the integral boundary layer equations in separated flow regions are analyzed and the connection between the mathematical singularities and the numerical ill-conditioning is discussed. It is shown that, by a suitable choice of closure relations, it is possible to obtain a boundary layer model free from numerical ill-conditioning in separated flow regions. The accuracy of the coupled viscous-inviscid model is investigated in a number of test cases including transitional and mildly separated flow over two different natural laminar flow airfoils and three-dimensional flow over a swept wing. It is concluded that the coupled method is able to provide reasonably accurate predictions of viscous and inviscid flow field quantities for the investigated cases.