Arbitrary Lagrangian-Eulerian method for Navier-Stokes equations with moving boundaries

Abstract

This article deals with the numerical approximation of Navier-Stokes equations in a domain with moving boundaries. Using the arbitrary Lagrangian-Eulerian (ALE) method we transform the problem from a moving domain to a fixed reference domain through an artificial domain velocity. Then, we apply the characteristic method to solve the Navier-Stokes equation in the fixed domain. Suitable boundary conditions are used for the interfaces. Three examples are provided to show the efficiency of the present method.