Arbitrary Lagrangian–Eulerian method for Navier–Stokes equations with moving boundaries Original Research Article

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.