Continuous Darcy-flux Approximations with Full Pressure Support for Structured and Unstructured Grids in 3D
H. Zheng and M.G. Edwards
Event name: ECMOR XI - 11th European Conference on the Mathematics of Oil Recovery
Session: Discretization Methods 1
Publication date: 08 September 2008
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This paper presents the development of families of control-volume distributed flux-continuous schemes with full control-volume surface pressure continuity for the general three dimensional pressure equation. Most effort to date has focused on schemes with pointwise continuity where the local continuity conditions are relatively compact. While full surface pressure continuity requires an increase in the number of local continuity conditions the new schemes prove to be relatively robust. Families of full pressure continuity schemes are developed here for structured and unstructured grids in three dimensions. The resulting Darcy flux approximations are applied to a range of three dimensional test cases that verify consistency of the schemes. Convergence tests of the three-dimensional families of schemes are presented, for a range of quadrature points. M-matrix conditions are presented and the schemes are tested for monotonicity. The full pressure continuity schemes are shown to be beneficial compared with earlier pointwise continuity schemes  both in terms improved monotonicity and convergence. The schemes are applied to challenging three dimensional test cases including heterogeneity for both structured and unstructured grids. TECHNICAL CONTRIBUTIONS Extension of full control-volume surface pressure continuity flux continuous schemes to structured and unstructured grids in three dimensions. M-matrix and monotonicity analysis of three dimensional methods. Benefits are demonstrated for challenging three dimensional test cases including heterogeneity on structured and unstructured grids.