Application of the finite element method to wave propagation problems

Abstract

In the past the numerical solution of unsteady Euler-flow type problems has been mainly achieved by the method of characteristics and finite difference techniques. The present paper is devoted to the finite element solution of the above mentioned problem: The partial differential equations are transformed into a corresponding variational problem, which by appropriate choice of the shape functions within a flow element, results to an initial value problem, consisting of a number n of ordinary differential equations for the introduced node variables with respect to the time t. One- and two-dimensional, including axis-symmetric, flow is being considered. Type of used elements, integration techniques and stability aspect of the numerical solution are one scope of the investigations, the other being a comparison to the finite difference technique. The results of these investigations prove that the finite element method can be considered to be a leading solution technique, especially with respect to the ease with which irregular geometries, non-uniform meshes and appropriate boundary conditions can be applied.