PhD thesisThe dispersion improved Compact Accurately Boundary Adjusting high- REsolution Technique (CABARET) schemes are presented as an upgrade of the original CABARET for improved wave propagation modeling. The new modification retains many attractive features of the original CABARET scheme such as shock-capturing and low dissipation. It is simple for implementation in the existing CABARET codes and leads to greater accuracy for solving linear wave propagation problems. A non-linear version of the dispersion-improved CABARET scheme is introduced to deal with contact discontinuities and shocks efficiently. The properties of the new linear and nonlinear CABARET schemes are analyzed for numerical dissipation and dispersion error based on Von Neumann analysis. The properties of the new linear and nonlinear CABARET schemes are demonstrated for one-dimensional, two-dimensional, and three-dimensional flows. Furthermore, the viscous terms in the full three-dimensional CABARET unstructured Navier-Stokes solver have been updated from the vertex approach to the collocated approach, resulting in efficient computational time
