The streamline-upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables, supplemented with shock-capturing, has been successfully used over a quarter of a century. In this paper, for inviscid compressible flows, the YZβ shock-capturing parameter, which was developed recently and is based on conservation variables only, is compared with an earlier parameter derived based on the entropy variables. Our studies include comparing, in the context of these two versions of the SUPG formulation, computational efficiency of the element- and edge-based data structures in iterative computation of compressible flows. Tests include 1D, 2D, and 3D examples.

Numerical simulations of viscous fingering instabilities in miscible displacements

SUMMARYWe present an implementation of an edge-based strategy together with an iterative adaptive implicit= explicit (AIE) time marching scheme for three-dimensional transport problems. The AIE algorithm treats part of the mesh as implicit and part as explicit, based on some stability and accuracy criteria. The solution of the implicit partition has its speed increased and memory requirements reduced by performing the matrix-vector products, within the iterative solver, edge-by-edge. Numerical examples show that the combined procedures can achieve signiÿcantly faster solutions than the usual fully implicit element-by-element approach.

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