Modelling of highly-heterogeneous media using a flux-vector-based Green element method (original) (raw)
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Geofluids, 2004
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Unsteady Flux-Vector-Based Green Element Method
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Journal of Computational and Applied Mathematics, 2013
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Combining finite volume and finite element methods to simulate fluid flow in geologic media
2003
Abstract The permeability, porosity, and fluid velocities that govern the flow of multi-phase fluids such as water, oil and steam in the earth's subsurface often vary over several orders of magnitude and the scales of interest vary from centimetres to kilometres. We describe a node-centred finite volume method coupled with a finite element method on an unstructured triangular grid to accurately and efficiently model multi-phase flow in geologic media.
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Journal of Computational and Applied Mathematics, 2016
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media. The method is based on divergence-conforming discontinuous Galerkin methods and overlapping, patch based domain decomposition smoothers. We show in benchmark experiments that the method is robust with respect to mesh size and contrast of permeability for highly heterogeneous media.
Combined Mixed Finite Element and Finite Volume for flow and transport in porous media
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2011
Appendix D. Integrations of the product of the interpolating functions and the fundamental solutions for surface and volume integrals as performed by MATHEMATICA software.. *set elems(all) *loop elems *Set var face1=((ElemsNum-1)*6+1) *Set var face2=((ElemsNum-1)*6+2) *Set var face3=((ElemsNum-1)*6+3) *Set var face4=((ElemsNum-1)*6+4) *Set var face5=((ElemsNum-1)*6+5) *Set var face6=((ElemsNum-1)*6+6) *format "%6i%8i%8i%8i%8i%8i%8i" *ElemsNum *Face1 *Face2 *Face3 *Face4 *Face5 *Face6 *end elems Faces Total: *Operation(6*nelem) Face |Elem |Node Stat Value |Node Stat Value |Node Stat Value |Node Stat Value | *set elems(hexahedra) *set var face=0 *set var Stat1=0 *set var Val1=0.0 *set Cond Flux *loop elems *set var face=face+1 *set var Nod1=elemsconec(1) *set var Nod2=elemsconec(4) *set var Nod3=elemsconec(3) *set var Nod4=elemsconec(2) *format "%4i%5i%5i%4i%12.5e%4i%4i%12.5e%4i%4i%12.5e%4i%4i%12.5e" *face