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Partitioned penalty methods for the transport equation in the evolutionary Stokes–Darcy‐transport problem
Author(s) -
Ervin V.,
Kubacki M.,
Layton W.,
Moraiti M.,
Si Z.,
Trenchea C.
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22303
Subject(s) - darcy–weisbach equation , darcy's law , mathematics , stokes flow , convergence (economics) , water transport , domain (mathematical analysis) , work (physics) , mathematical optimization , convection–diffusion equation , flow (mathematics) , coupling (piping) , stokes problem , finite element method , water flow , mathematical analysis , porous medium , geometry , physics , geology , geotechnical engineering , porosity , mechanical engineering , economic growth , engineering , economics , thermodynamics
There has been a surge of work on models for coupling surface‐water with groundwater flows which is at its core the Stokes–Darcy problem, as well as methods for uncoupling the problem into subdomain, subphysics solves. The resulting (Stokes–Darcy) fluid velocity is important because the flow transports contaminants. The numerical analysis and algorithm development for the evolutionary transport problem has, however, focused on a quasi‐static Stokes–Darcy model and a single domain (fully coupled) formulation of the transport equation. This report presents a numerical analysis of a partitioned method for contaminant transport for the fully evolutionary system. The algorithm studied is unconditionally stable with one subdomain solve per step. Numerical experiments are given using the proposed algorithm that investigates the effects of the penalty parameters on the convergence of the approximations.