A Space Time Domain Decomposition Approach using Enhanced Velocity Mixed Finite Element Method

TL;DR

This paper introduces a space-time domain decomposition method based on enhanced velocity mixed finite element techniques, enabling different discretizations on subdomains while maintaining mass conservation, applicable to various flow and transport problems in porous media.

Contribution

It extends the enhanced velocity mixed finite element method to a space-time domain decomposition framework with a monolithic solution approach, avoiding subdomain iterations and handling nonlinearities effectively.

Findings

Accurately resolves advection-diffusion features in heterogeneous media.

Circumvents nonlinear solver convergence issues with large time steps.

Demonstrates applicability to single phase, slightly compressible, and multiphase flow problems.

Abstract

A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time discretizations on non-overlapping, subdomains by enforcing a mass continuity argument at the non-matching interface to preserve the local mass conservation property inherent to the mixed finite element methods. To this effect, we consider three different model formulations: (1) a linear single phase flow problem, (2) a non-linear slightly compressible flow and tracer transport, and (3) a non-linear slightly compressible, multiphase flow and transport. We also present a numerical solution algorithm for the proposed domain decomposition approach where a monolithic (fully coupled in space and time) system is constructed that does not require subdomain iterations. This space-time EVMFE method accurately resolves advection-diffusion transport features, in a heterogeneous medium, while circumventing non-linear solver convergence issues associated with large time-step sizes for non-linear problems. Numerical results are presented for the aforementioned, three, model formulations to demonstrate the applicability of this approach to a general class of problems in flow and transport in porous media.