Postprocessing of Non-Conservative Flux for Compatibility with Transport in Heterogeneous Media

TL;DR

This paper introduces a flux postprocessing method that ensures conservation in flow models, improving accuracy in heterogeneous media by using a weighted norm and analyzing boundary flux effects.

Contribution

A novel conservative flux postprocessing algorithm that maintains convergence order and enhances results in heterogeneous media using a weighted $L^2$ norm.

Findings

Postprocessed flux matches original flux convergence order.

Weighted norm improves results in heterogeneous media.

Analysis of boundary flux effects on coupled flow and transport.

Abstract

A conservative flux postprocessing algorithm is presented for both steady-state and dynamic flow models. The postprocessed flux is shown to have the same convergence order as the original flux. An arbitrary flux approximation is projected into a conservative subspace by adding a piecewise constant correction that is minimized in a weighted $L^2$ norm. The application of a weighted norm appears to yield better results for heterogeneous media than the standard $L^2$ norm which has been considered in earlier works. We also study the effect of different flux calculations on the domain boundary. In particular we consider the continuous Galerkin finite element method for solving Darcy flow and couple it with a discontinuous Galerkin finite element method for an advective transport problem.