Three-dimensional ALE-FEM method for fluid flow in domains with moving boundaries part II: accuracy and convergence

Abstract

An arbitrary Lagrangian-Eulerian numerical method for the numerical simulations of fluid flow in three-dimensional time dependent domains that uses a fixed computational mesh locally fitted to the position of the moving interfaces is examined from the point of view of its accuracy and convergence properties. Elements adjacent to the moving interfaces continuously change shape to fit the moving interfaces to correctly describe the position and shape of the moving interfaces. These elements are used in conjunction with the rest of the mesh elements in the calculations. How changes in the mesh affect the accuracy of the results is examined through truncation error analysis and numerical simulations. The accuracy of the calculations is not adversely affected by the continuous mesh deformation it is shown; the convergence rate of this method is second order. The behaviour of the local error of moving interfaces exhibits the same accuracy as all the domains.