Numerical solution of the eulerian equations of compressible flow by a finite element method which follows the free boundary and the interfaces

Abstract We describe a numerical method to compute the solution of a system of conservation laws subject to an initial condition and certain boundary conditions which involve a free boundary. This method is specially designed to solve the Eulerian equations of compressible flow. It is based on finite elements relative to the space variables and the time; the elements near the boundary (or the interfaces) are chosen in such a way that they follow the boundary (or the interfaces); the choice of the interior elements is arbitrary at each time step. For the computation of discontinuous solutions (shocks), we introduce a special type of pseudoviscosity. Numerical results are given.