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.

Development of an embedded discrete fracture model for 2D and 3D unstructured grids using an element-based finite volume method

“…Unstructured grids have been used in reservoir simulation to represent geologically complex reservoirs (Fung et al, 1992;Durlofsky and Chien, 1993;Verma and Aziz, 1997;Prévost et al, 2002Prévost et al, , 2005Edwards, 2002;Hoteit and Firoozabadi, 2006a;Vitel and Souche, 2007;Sepehrnoori, 2007, 2010;Araújo et al, 2016;Fernandes et al 2016Fernandes et al , 2017Samier and Masson, 2017). In comparison with structured grids, unstructured grids are more capable of representing irregular reservoir structures and reservoir boundaries, as they provide more flexibility regarding the geometry of gridblocks and their discretization.…”

“…There are several types of numerical approximation schemes used for unstructured grids, including the finite volume method (Fung et al, 1992;Edwards, 2002;Marcondes et al, 2013;Fernandes et al, 2017), finite element method, and mixed finite element method (Durlofsky and Chien, 1993;Hoteit and Firoozabadi, 2006). The control-volume finite element method (CVFEM) (Baliga and Patankar, 1980;Forsyth, 1990;Fung et al, 1992) is also a widely used numerical approximation scheme for unstructured grids.…”