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:
- 10.1016/0021-9991(75)90100-X
- Bibcode:
- 1975JCoPh..18...21J
- Keywords:
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- Compressible Flow;
- Conservation Laws;
- Euler Equations Of Motion;
- Finite Element Method;
- Free Boundaries;
- Hydrodynamic Equations;
- Boundary Conditions;
- Boundary Value Problems;
- Liquid-Liquid Interfaces;
- Shock Discontinuity;
- Viscous Fluids;
- Fluid Mechanics and Heat Transfer