Higher order Godunov schemes for gas dynamics

The starting point for this work is the method of Bell, Colella and Trangenstein (BCT) which retained the earlier predictor-corrector formulation of Colella and Woodward, Colella and Glaz but replaced the 'exact' Riemann problem iteration and Godunov flux with a linearized approximate phase space decomposition and a variant of the Engquist-Osher flux.;In my thesis, the BCT method is used to solve problems in gas dynamics in one and two space dimensions, with particular emphasis on the nonconvex equation of state (EOS) case. The most important results are for the full 3 x 3 system and will be presented here. In terms of numerical analysis, the main objective is validation of the method by direct comparison with older 2nd-order Godunov results and experimental data. Of particular importance is studying the flux function and the special techniques for nonconvex EOS; here, I also compare BCT with another related scheme due to Zachary, Malagoli and Colella which handles the flux differently.;In this thesis, the numerical results include: (1) direct comparison with exact solution in 1D, (2) computations of 2D Riemann problems, (3) computations of shock wave diffraction at a straight corner (step), and (4) computations of oblique shock wave interactions and related problems. Realistic and complicated real gas EOS are used.