An interacting viscous-inviscid method for efficiently computing steady and unsteady low Mach number viscous flows with separation is presented. The inviscid region is modeled using a finite element discretization of the full potential equation. The viscous region is modeled using a finite difference boundary layer technique. The two regions are simultaneously coupled through the requirement that the edge velocities of the two regions be equal, and through an injection velocity arising the displacement thickness. For unsteady flows, the fluid is assumed to be composed of two parts: a mean or steady flow plus a harmonically varying small unsteady disturbance. This assumption results in a nonlinear description for the mean flow, and a linear description for the small disturbance unsteady flow. For the solution of the mean flow, the nonlinear governing equations are reduced to a series of linear matrix equations using Newton iteration. The resulting mean flow solution is then used to form the variable coefficients of the linearized unsteady equations, which are solved directly. The present method is able to compute flows with separation, and in the case of unsteady flows, flows with moving separation and reattachment points. © 1995 by Academic Press, Inc.