The edge-based face element method for 3D-stream function and flux calculations in porous media flow
article
We present a velocity-oriented discrete analog of the partial differential equations governing porous media flow: the edge-based face element method. Conventional finite element techniques calculate pressures in the nodes of the grid. However, such methods do not satisfy the requirement of flux continuity at the faces. In contrast, the edge-based method calculates vector potentials along the edges, leading to continuity of fluxes. The method is algebraically equivalent with the popular block-centered finite difference method and with the mixed-hybrid finite element method, but is algorithmically different and has the same robustness as the more conventional node-based velocity-oriented method. The numerical examples are computed analytically and may, therefore, be considered as an 'heuristic proof' of the theory and its practical applicability for reservoir engineering and geohydrology. © 2004 Kluwer Academic Publishers. Printed in the Netherlands.
Topics
3D-stream functionDiscrete analogsEdge-based vector potentialsFace elementsVelocity-oriented approachComputational methodsFinite element methodHeuristic methodsHydrogeologyPartial differential equationsPorous materialsRobustness (control systems)VectorsEdge-based face element methodFlux continuityStream flowfinite difference techniqueflow modelingporous medium
TNO Identifier
237822
ISSN
01693913
Source
Transport in Porous Media, 55(3), pp. 361-382.
Pages
361-382
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