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This paper presents a computational scheme for compressible magnetohydrody-namics (MHD). The scheme is based on the same elements that make up many modern compressible gas dynamics codes: a high-resolution upwinding based on an approximate Riemann solver for MHD and limited reconstruction; an optimally smoothing multi-stage time-stepping scheme; and(More)
This paper reports progress towards high-order fluctuation-splitting schemes for the Navier-Stokes Equations. High-order schemes we examined previously are all based on gradient reconstruction, which may result in undesired mesh-dependency problem due to the somewhat ambiguous gradient reconstruction procedures. Here, we consider schemes for P2 elements in(More)
Operational problems and system damage have been linked to the flow regime transition between free surface and pressurized flow in rapidly filling stormwater and combined sewer systems. In response, emphasis has been placed on the development of numerical models to describe hydraulic bores and other flow phenomena that may occur in these systems. Current(More)
order accurate discontinuous discontinuous nite element solution of the 2D Euler equations, A massively parallel adaptive nite element method with dynamic load balancing, SAND 93-0936C (1993). 21. K. Eriksson and C. Johnson, Adaptive nite element methods for parabolic problems I: A linear model problem, SIAM J. Adaptive nite element methods for parabolic(More)
Professor Bram van Leer, for the help they have given me to complete this work. They both tolerated my thrashing through various research topics, in my quest to `re-invent CFD,' and both were there when I returned somewhat humbled. I would also like to thank Professor Ken Powell for answering my questions over the years, and for being on my committee.(More)
Some techniques for improving the accuracy of multidimensional up-wind uctuation distribution schemes for the scalar advection equation are compared. One involves the construction of a consistent Petrov-Galerkin nite element scheme which is equivalent to the uctuation distribution scheme when mass-lumping is applied. Another uses a predictor-corrector(More)