A Fast Solver for Navier–Stokes Equations in the Laminar Regime Using Mortar Finite Element and Boundary Element Methods

Abstract

A multistep method is used to solve the Navier–Stokes equations, formulated with vorticity and stream function. Each time step is decomposed into three stages: a convection step using the characteristic-Galerkin method, a diffusion step decomposed into a shift to remove the right-hand side, and a linear homogeneous generalized Stokes problem solved by a boundary element method. A domain decomposition method is implemented with nonconforming mortar elements. In each subdomain we use a finite element method with isoparametric or overparametric quadrilateral elements. The quadrangulations for $\omega $ and for $\psi $ are not necessarily the same. The boundary element method computes $\omega $ at the boundary but at high Reynolds number it can be replaced by an asymptotic formula. We present numerical tests for flows around cylinders and wing profiles. Results are compared to other authors’ and the validity of the asymptotic formula is investigated.