Comparison of cell- and vertex-centered finite-volume schemes for flow in fractured porous media

TL;DR

This paper compares various finite volume numerical schemes for simulating flow in fractured porous media, introducing two new vertex-centered methods that are efficient and accurate.

Contribution

It presents two novel vertex-centered finite volume schemes and compares them with existing methods in terms of convergence and computational efficiency.

Findings

New schemes are in good agreement with established methods.

The novel approaches are computationally less expensive on unstructured grids.

All methods show reliable convergence behavior.

Abstract

Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a response to this, an active field of research has developed over the past decades, focussing on the development of mathematical models and numerical methods to describe and simulate the flow processes in fractured rock. In this work, we present a comparison of different finite volume-based numerical schemes for the simulation of flow in fractured porous media by means of numerical experiments. Two novel vertex-centered approaches are presented and compared to well-established numerical schemes in terms of convergence behaviour and their performance on benchmark studies taken from the literature. The new schemes show to produce results that are in good agreement with those of established methods while being computationally less expensive on unstructured simplex grids.