Solution of three-dimensional unsteady external flow using a coupled arbitrary Lagrangian FEM–BEM model

Abstract

A computational model has been developed in this paper to solve three-dimensional unsteady incompressible viscous flow problems in external flow fields. The model is based on primitive variables in Navier–Stokes equations under transient conditions. The model can be used to solve infinite boundary value problems by extracting the boundary effects on a specified finite computational domain using projection method of the Navier–Stokes equations. The momentum equation of fluid motion is solved using the three-step finite element method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation by considering the pressure to be zero at the infinite boundary. Arbitrary Lagrangian–Eulerian method is incorporated in the present model to solve the moving boundary problems. The model has been applied initially to simulate a cubic cavity flow problem for verification purpose and further used to simulate the flow past a square cylinder in two dimensions. Finally, the external flow problem of flow induced by the movement of a sphere inside a viscous flow field in three dimensions has also been considered. The simulation results are found to be reasonable and satisfactory.