Resolution Numerique des Equations Deuler pour les Fluides Compressibles Par des Methodes Delements Finis (Numerical Solution of the Euler Equations for Compressible Fluids by the Finite Element Method)

摘要

A second order approach based on the extension of the Lax, Wendroff, and Richtmyer method to the variational Galerkin procedure is presented. Triangular Lagrangian elements are chosen. The stability is analyzed in a simplified context (scalar and linear), but for arbitrary triangulation. The approximation is continuous and centered. The solution is stabilized using an artificial viscosity, which allows the comparison of the method with the utilization of centered finite differences. It is shown that the second order method is robust and allows the detection of shock, converging in 500 iterations.