A space–time domain decomposition approach using enhanced velocity mixed finite element method

• Published in: Journal of computational physics Vol. 374; no. C; pp. 893 - 911
• Main Authors: Singh, Gurpreet, Wheeler, Mary F.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.12.2018; Elsevier Science Ltd; Elsevier
• Subjects: Compressible flow; Computational physics; Domain decomposition methods; Enhanced velocity; Finite element analysis; Finite element method; Formulations; Fully-implicit; Mathematical analysis; Mathematical models; Mixed finite element; Monolithic system; Multiphase flow; Nonlinear equations; nuclear (including radiation effects), carbon sequestration; Porous media; Spacetime; Space–time domain decomposition; Time domain analysis; Transport; Velocity; Space–time domain decomposition; Mixed finite element; Monolithic system; Enhanced velocity; Fully-implicit
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2018.08.013

A space–time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE), introduced by Wheeler et al. in (2002) [26], for spatial domain decomposition. The proposed approach allows for different space–time discretizations on non-overlapping, subdomains by enforcing a mass continuity at non-matching interfaces to preserve local mass conservation 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 flow and transport problems in porous media. •Space time domain decomposition for spatial and temporal refinements in subdomains.•Fully implicit, monolithic, space–time solver.•Circumvent Newton convergence and small time-step size issues for non-linear PDEs.•Numerical results for scientific and practical problems of interest in porous medium.