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Multidimensional Improvements to the NAG Riemann Solvers

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The NAG Library contains routines for solving the partial differential equations specific to compressible, ideal fluid flow. These equations are generally written in conservation law form where the conserved quantities are mass density, momentum and total energy of the fluid.  This set of equations can be solved using a finite volume technique that considers each conserved variable as a volume average over a finite volume (typically a small cube) and sums the fluxes (flow rates per unit area) computed at the faces surrounding the volume to get the total rate of change of a particular variable for that volume.

Several methods exist to solve this set of coupled equations (e.g. Flux Corrected Transport, ENO and WENO schemes, etc.). I focus here on the Godunov method where, in its simplest form, the fluxes are computed by solving a Riemann problem at the interface between two cells in the computational mesh. In such methods, appropriately limited (I do not address limiting procedures here…