A Control-Volume, Finite-Element Method for Local Mesh Refinement in Thermal Reservoir Simulation

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Abstract
Summary: This paper describes a control-volume, finite-element technique for coupling coarse grids with local fine meshes. The pressure is treated in a finite-element manner, while the mobility terms are upstream weighted in the usual way. This requires identification of the cell volumes and edges that are consistent with the linear finite-element discretization of the pressure. To ensure that the pressure equation yields an M matrix, various conditions are required for the type of triangulation allowed. Because the form of the equations is similar to the usual finite-difference discretization, standard techniques can be used to solve the Jacobian. The local mesh-refinement method is demonstrated on some thermal reservoir simulation problems, and computational results are presented. Significant savings in execution times are obtained while predictions similar to global fine-mesh runs are given.

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