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.
 Publication:

Journal of Computational Physics
 Pub Date:
 May 1975
 DOI:
 10.1016/00219991(75)90100X
 Bibcode:
 1975JCoPh..18...21J
 Keywords:

 Compressible Flow;
 Conservation Laws;
 Euler Equations Of Motion;
 Finite Element Method;
 Free Boundaries;
 Hydrodynamic Equations;
 Boundary Conditions;
 Boundary Value Problems;
 LiquidLiquid Interfaces;
 Shock Discontinuity;
 Viscous Fluids;
 Fluid Mechanics and Heat Transfer