Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics
Journal of Computational Physics
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On postshock oscillations due to shock capturing schemes in unsteady flows
Journal of Computational Physics
Computations of slowly moving shocks
Journal of Computational Physics
Hole-Cutting for Three-Dimensional Overlapping Grids
SIAM Journal on Scientific Computing
Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
Journal of Computational Physics
A matrix stability analysis of the carbuncle phenomenon
Journal of Computational Physics
The design of flux-corrected transport (fct) algorithms on structured grids
The design of flux-corrected transport (fct) algorithms on structured grids
Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow
Journal of Computational Physics
A high-resolution Godunov method for compressible multi-material flow on overlapping grids
Journal of Computational Physics
Accurate monotonicity- and extrema-preserving methods through adaptive nonlinear hybridizations
Journal of Computational Physics
On sub-linear convergence for linearly degenerate waves in capturing schemes
Journal of Computational Physics
Journal of Computational Physics
Failsafe flux limiting and constrained data projections for equations of gas dynamics
Journal of Computational Physics
Richardson Extrapolation for Linearly Degenerate Discontinuities
Journal of Scientific Computing
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This study considers the development and assessment of a flux-corrected transport (FCT) algorithm for simulating high-speed flows on structured overlapping grids. This class of algorithm shows promise for solving some difficult highly-nonlinear problems where robustness and control of certain features, such as maintaining positive densities, is important. Complex, possibly moving, geometry is treated through the use of structured overlapping grids. Adaptive mesh refinement (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. Simulation results are obtained for a set of test problems and the convergence characteristics are demonstrated and compared to a high-resolution Godunov method. The problems considered are 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 inclined plane.