| Abstract: | A class of shock-capturing Petrov–Galerkin finite element methods that use high-order non-oscillatory interpolations is presented for the one-dimensional compressible Euler equations. Modified eigenvalues which employ total variation diminishing (TVD), total variation bounded (TVB) and essentially non-oscillatory (ENO) mechanisms are introduced into the weighting functions. A one-pass Euler explicit transient algorithm with lumped mass matrix is used to integrate the equations. Numerical experiments with Burgers' equation, the Riemann problem and the two-blast-wave interaction problem are presented. Results indicate that accurate solutions in smooth regions and sharp and non-oscillatory solutions at discontinuities are obtainable even for strong shocks. |
