... pressure equation arbogast Artificial Intelligence Fluid Dynamics mixed finite element method society of petroleum engineers dimension grid block saturation equation Introduction Standard finite volume methods used widely in reservoir simulators are accurate to relatively low order...

... Abstract A robust and efficient simulation technique is developed based on the extension of the mimetic finite volume method to multiscale hierarchical hexahedral (corner-point) grids via use of the multiscale mixed finite element method. The implementation of the mimetic subgrid discretization...

... fluxes and can be viewed within a variational framework as a mixed finite element method with special approximating spaces and quadrature rules. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. The framework allows...

... mixed finite element method Introduction Abstract This paper presents multiblock methods for coupled multiphase flow and species transport modeling in porous media applications. These methods provide local mass conservation and a continuous approximation of fluxes across inter-element faces...

... an appropriate numerical quadrature to localize the mixed finite element method into a cell-centered finite difference method. For diagonal tensor coefficients, we recover the usual 7-point stencil. For full tensors, the method leads to a 27-point stencil of multipoint flux approximation (MPFA) methods...

... research has shown, however, that MPFA methods may lead to unphysical nonmonotonic solutions for high anisotropy ratios or strongly distorted grids. In this paper, we work in the mathematical framework of mixed finite element methods (MFEM). We study a low- and high-order accurate MFEM, based...

.... The equivalence of the block-centred finite difference method to a particular class of mixed finite element method (see Russell and Wheeler 4 , for a review) has led us to a simple and natural generalisation of the usual approach for the orthogonal case. Our algorithm extends the usual mixed finite element...

... and suboptimal use of upstream weighting of transport terms combine to cause many aspects of the numerical dispersion and grid orientation problems. A mixed finite element method has been developed to obtain more accurate approximations to the fluid velocities. In this method the Darcy velocities are considered...

... can also be formulated. Since the computed fluid velocities help to determine the time-stepping procedure in the characteristic-based method and since accurate velocities are crucial in the method's ability to conserve mass, very accurate Darcy velocities are necessary. A mixed finite element method...