Convergence study of a family of flux‐continuous, finite‐volume schemes for the general tensor pressure equation

Abstract

Abstract In this paper, a numerical convergence study of family of flux‐continuous schemes is presented. The family of flux‐continuous schemes is characterized in terms of quadrature parameterization, where the local position of continuity defines the quadrature point and hence the family. A convergence study is carried out for the discretization in physical space and the effect of a range of quadrature points on convergence is explored. Structured cell‐centred and unstructured cell‐vertex schemes are considered. Homogeneous and heterogeneous cases are tested, and convergence is established for a number of examples with discontinuous permeability tensor including a velocity field with singularity. Such cases frequently arise in subsurface flow modelling. A convergence comparison with CVFE is also presented. Copyright © 2006 John Wiley & Sons, Ltd.