A Space Time Domain Decomposition Approach using Enhanced Velocity Mixed Finite Element Method
This work provides a monolithic space-time domain decomposition approach for flow and transport in porous media, addressing convergence issues for large time steps in nonlinear problems.
The paper extends the enhanced velocity mixed finite element method to space-time domain decomposition, enabling different space-time discretizations on subdomains while preserving local mass conservation. Numerical results for linear and nonlinear flow and transport problems demonstrate accurate resolution of advection-diffusion features and avoidance of nonlinear solver convergence issues.
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.