SFB 1313 Publication "A finite-volume moving-mesh method for two-phase flow in fracturing porous media"

New SFB 1313 publication (University of Stuttgart), published in the Journal of Computational Physics. The paper has been developed in the framework of SFB 1313's research project B03.

"A finite-volume moving-mesh method for two-phase flow in fracturing porous media"

Authors

• Samuel Burbulla (University of Stuttgart, SFB 1313 research project B03)
• Christian Rohde (University of Stuttgart, SFB 1313 research projects B03 and C02)

Abstract

Multiphase flow in fractured porous media can be described by discrete fracture matrix models that represent the fractures as dimensionally reduced manifolds embedded in the bulk porous medium. Generalizing earlier work on this approach we focus on immiscible two-phase flow in time-dependent fracture geometries, i.e., the fracture itself and the aperture of the fractures might evolve in time. For dynamic fracture geometries of that kind, neglecting capillary forces, we deduce by transversal averaging of a full dimensional description a dimensionally reduced model that governs the geometric evolution and the flow dynamics. The core computational contribution is a mixed-dimensional finite-volume discretization based on a conforming moving-mesh ansatz. This finite-volume moving-mesh (FVMM) algorithm is tracking the fractures' motions as a family of unions of facets of the mesh. Notably, the method permits arbitrary movement of facets of the triangulation while keeping the mass conservation constraint. In a series of numerical examples we investigate the modeling error of the reduced model as it compares to the original full dimensional model. Moreover, we show the performance of the finite-volume moving-mesh algorithm for the complex wave pattern that is induced by the interaction of saturation fronts and evolving fractures.

Links

• SFB 1313 research project B03 "Heterogeneous multi-scale methods for two-phase flow in dynamically fracturing porous media"
• SFB 1313 Publication "A finite-volume moving-mesh method for two-phase flow in fracturing porous media"