Use of algebraic dual representations in domain decomposition methods for Darcy flow in 3D domain

TL;DR

This paper introduces algebraic dual representations combined with domain decomposition methods for 3D Darcy flow, leading to more memory-efficient and faster simulations despite increased unknowns.

Contribution

It develops a novel approach using algebraic dual representations in domain decomposition for Darcy equations, improving computational efficiency.

Findings

Reduced memory usage compared to continuous Galerkin methods

Faster simulation times despite more unknowns

Effective in both manufactured and real reservoir models

Abstract

In this work we use algebraic dual representations in conjunction with domain decomposition methods for Darcy equations. We define the broken Sobolev spaces and their finite dimensional counterparts. In addition, a global trace space is defined that connects the solution between the broken spaces. Use of dual representations results in a sparse metric free representation of the constraint on divergence of velocity, the pressure gradient term and on the continuity constraint across the sub domains. To demonstrate this, we solve two test cases: i) manufactured solution case, and ii) industrial benchmark reservoir modelling problem SPE10. The results demonstrate that the domain decomposition scheme, although with more unknowns, requires less memory and simulation time as compared to the continuous Galerkin formulation.