Fast and accurate domain decomposition methods for reduced fracture models with nonconforming time grids

TL;DR

This paper introduces fast, accurate, and convergent domain decomposition methods for simulating fluid flow in fractured porous media, allowing different time step sizes in fractures and surrounding regions to improve computational efficiency.

Contribution

The paper develops novel global-in-time domain decomposition methods with nonconforming time grids for reduced fracture models, enhancing convergence and accuracy.

Findings

Methods achieve faster convergence with efficient preconditioners.

Numerical results demonstrate improved performance in 2D fracture problems.

Nonconforming grids preserve accuracy while reducing computational cost.

Abstract

This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous medium. We aim to develop fast-convergent and accurate global-in-time domain decomposition (DD) methods for such a reduced fracture model, in which smaller time step sizes in the fracture can be coupled with larger time step sizes in the subdomains. Using the pressure continuity equation and the tangential PDEs in the fracture-interface as transmission conditions, three different DD formulations are derived; each method leads to a space-time interface problem which is solved iteratively and globally in time. Efficient preconditioners are designed to accelerate the convergence of the iterative methods while preserving the accuracy in time with nonconforming grids. Numerical results for two-dimensional problems with non-immersed and partially immersed fractures are presented to show the improved performance of the proposed methods.