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Joint work with G.E. Fladmark, H. Reme, G. Å. Øye, Department of Mathematics, University of Bergen, Bergen, Norway,
This paper is based on a finite volume formulation of a thermal multiphase, compositional model in three space dimensions.
We have chosen to use a sequential solution procedure. This means that we solve for the pressure/velocity in a first step and then solve updated molar mass and temperature equations in a second step. Saturations for the fluids are calculated from the thermodynamic model in a third step. An important part of the work is adaptive local refinement at faults and highly fractured zones, based on domain decomposition type of methods. This technique is implemented both for the pressure/velocity part as well as the flow part of the model.
In general, a porous medium is anisotropic as well as heterogeneous. Continuity in both the flux and potential across a surface is hard to achieve in a numerical approximation of such models. Recently multipoint flux methods have been developed and these techniques give better results than standard two point approximations.
Local grid refinement gives a nonmatching mesh environment and a multipoint flux approximation for nonmatching grids will be presented. Numerical results, where two-point and multi-point flux approximations are compared, will be given. Also, large scale computations will be shown.
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