CPR MethodByGustavo Galindez Ramirez

Advisors: Paulo R. M. Lyra Darlan K. E. de Carvalho.

OutlineSaturation solverCPR Method 1D 2DPressure solverMixed Finite ElementStreamlines Sequential splitting method (IMPES)

Framework of the CPR formulation

Framework of the CPR formulation. . .. . .

Results

MappingPhysical DomainReference Domain

Mixed Finite-ElementMFE solve for velocity and pressure simultaneously, resulting in a more accurate velocity field than for finite differences and standard finite elements.A continuously defined velocity field is obtained only for MFE method.For the others methods, such as: FD,FEM, FV(MPFA-CVFE) methods one must use an interpolation scheme to determine the velocity from the discrete fluxes at the cell edges (Haegland et. al. 2007)

Mixed Finite-Element-Streamlines

MFE-Mapping-StreamlinesIsoparametric mappingPollocks Method - Piola transform

CPR + MFEIMPES

FV-Mapping-StreamlinesThree different partitions for the quadrilateralStreamlines traced for different triangulations.

ReferencesH. Haegland, H.K. Dahle, G.T. Eigestad, K. A. Lie and I. Aavatsmark. Improved streamlines and time-of-flight for streamline simulation on irregular grids. Advanced in Water Resourses 30 (2007) 1027-1045.H. T. Huynh. A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods. 18th AIAA Computational Fluid Dynamics Conference 25-28 June 2007, Miami, FL.Jorg E. Aarmes, Tore Gimse and Kunt-Andreas Lie. An Introduction to the Numerics of Flow in Porous Media using Matlab. SINTEF ICT, Dept. of Applied Mathematics, Oslo.Sbastien F. Matringe, Ruben Juanes and Hamdi A. Tchelepi. Robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids. Journal of Computational Physics 219 (2006) 992-1012.Z. J. Wang, H. Gao and T. Haga. A Unifying Discontinuous Formulation for Hybrid Meshes. World Scientific Review, 2010.Zimmerman, Ben James. The Efficient Implementation of Correction Procedure via Reconstruction with GPU Computing (2013).Graduate Theses and Dissertations. Paper 13102.