Nonoscillatory shockcapturing finite element methods for the onedimensional compressible Euler equations
Abstract
A class of shockcapturing PetrovGalerkin finite element methods that use highorder nonoscillatory interpolations is presented for the onedimensional compressible Euler equations. Modified eigenvalues which employ total variation diminishing (TVD), total variation bounded (TVB) and essentially nonoscillatory (ENO) mechanisms are introduced into the weighting functions. A onepass Euler explicit transient algorithm with lumped mass matrix is used to integrate the equations. Numerical experiments with Burgers' equation, the Riemann problem and the twoblastwave interaction problem are presented. Results indicate that accurate solutions in smooth regions and sharp and nonoscillatory solutions at discontinuities are obtainable even for strong shocks.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 September 1990
 DOI:
 10.1002/fld.1650110405
 Bibcode:
 1990IJNMF..11..405Y
 Keywords:

 Compressible Flow;
 Computational Fluid Dynamics;
 Essentially NonOscillatory Schemes;
 Euler Equations Of Motion;
 Finite Element Method;
 One Dimensional Flow;
 Galerkin Method;
 Tvd Schemes;
 Fluid Mechanics and Heat Transfer