An evaluation of the FCT method for high-speed flows on structured overlapping grids

This study focuses on the development and assessment of a Flux-Corrected Trans-port(FCT) algorithm for simulating high-speed flows on structured overlapping meshes. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as main-taining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping meshes and adaptive mesh refine-ment (AMR) is employed to ensure sharp resolution of discontinuities in an efficient manner. Improvements to the FCT algorithm are proposed for the treatment of strong rarefaction waves as well as rarefaction waves containing a sonic point. The order-of-accuracy of the FCT method is demonstrated through convergence studies for smooth manufactured solutions. Simulation results are obtained for a set of test problems and the convergence characteristics of the method demonstrated. Com-parison to a high-resolution Godunov method provides more details concerning the performance of FCT for overlapping mehes. The set of problems considered here includes an isolated shock, an isolated contact, a modified Sod shock tube problem, a two shock Riemann problem, the Shu-Osher test problem, shock impingement on single cylinder, and irregular Mach reflection of a strong shock striking an incline plane