Volume 57, Number 3, May-June 2023
|Page(s)||1257 - 1296|
|Published online||12 May 2023|
A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem
Oakland University, Department of Mathematics and Statistics, Rochester Hills, MI 48307, USA
2 University of Waterloo, Department of Applied Mathematics, Waterloo, ON, Canada
* Corresponding author: firstname.lastname@example.org
Accepted: 13 February 2023
We present a high-order hybridized discontinuous Galerkin (HDG) method for the fully coupled time-dependent Stokes–Darcy-transport problem where the fluid viscosity and source/sink terms depend on the concentration and the dispersion/diffusion tensor depends on the fluid velocity. This HDG method is such that the discrete flow equations are compatible with the discrete transport equation. Furthermore, the HDG method guarantees strong mass conservation in the Hdiv sense and naturally treats the interface conditions between the Stokes and Darcy regions via facet variables. We employ a linearizing decoupling strategy where the Stokes/Darcy and the transport equations are solved sequentially by time-lagging the concentration. We prove well-posedness and optimal a priori error estimates for the velocity and the concentration in the energy norm. We present numerical examples that respect compatibility of the flow and transport discretizations and demonstrate that the discrete solution is robust with respect to the problem parameters.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 76D07 / 76S99
Key words: Stokes/Darcy flow / coupled flow and transport / advection–diffusion / hybridized methods / discontinuous Galerkin / multiphysics
© The authors. Published by EDP Sciences, SMAI 2023
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