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Fluids 2017, 2(3), 47;

Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater–Surface Water Flows

Department of Mathematics, Middlebury College, Middlebury, VT 05753, USA
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Author to whom correspondence should be addressed.
Received: 1 July 2017 / Revised: 22 August 2017 / Accepted: 26 August 2017 / Published: 10 September 2017
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)
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We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized for each sub-flow. This strategy often results in a time-step condition for stability. Furthermore, small problem parameters, specifically those related to the physical characteristics of the porous media domain, can render certain time-step conditions impractical. Despite these obstacles, researchers have made significant progress towards efficient, stable, and accurate partitioned methods. Herein, we provide a comprehensive survey and comparison of recent developments utilizing these non-iterative numerical schemes. View Full-Text
Keywords: implicit-explicit schemes; finite difference methods; Stokes–Darcy equations implicit-explicit schemes; finite difference methods; Stokes–Darcy equations

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Kubacki, M.; Tran, H. Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater–Surface Water Flows. Fluids 2017, 2, 47.

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