A TVD scheme for 3D unstructured grids applied to compositional reservoir simulation

Abstract

In reducing the grid orientation effect for the numerical solution of partial differential equations, interpolation functions play an important role when the advective transport of the governing equations is considered. This is due to the fact that, in general, the unknowns are evaluated in the vertices of the elements and such properties must be extrapolated to inner parts of the elements. First-order schemes, such as upwind, are the easiest methods to use for performing the extrapolation of the properties. However, such methods introduce a large amount of numerical diffusion in the solution. A few higher-order interpolation schemes, on the other hand, are capable of providing solutions free of numerical diffusion, increasing the accuracy of the method and reducing the computational efforts required. In this work, we investigate the TVD interpolation scheme for three-dimensional unstructured grids in conjunction with Element-based Finite Volume Method (EbFVM) using four types of elements: hexahedron, tetrahedron, prism and pyramid.