Journal Article10.1002/num.23022
An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows
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TL;DR: In this paper , the authors proposed a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier-Stokes-Darcy equations that model the coupling surface and groundwater flows, and verified the stability and second-order convergence of the algorithm from theoretical analysis and numerical experiments.
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Abstract: In this article, we propose a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier‐Stokes/Darcy equations that model the coupling surface and groundwater flows. It uncouples the surface from the groundwater flow by the Crank‐Nicolson Leapfrog scheme for the discretization in time, and through the artificial compression method without artificial pressure boundary conditions to decouple the velocity and pressure of the incompressible flow. Finally, we have verified the stability and second‐order convergence of the algorithm from theoretical analysis and numerical experiments.
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Citations
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TL;DR: Analysis of a new adaptive time filter algorithm for the unsteady Stokes/Darcy model TLDR: A new adaptive time filter algorithm is proposed for the unsteady Stokes/Darcy model, which improves the convergence order to the second order and enhances computational efficiency.
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A Low‐Cost, Second‐Order Artificial Compression Method for Incompressible Navier–Stokes Equations
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A Two-Grid Method of a Mixed Stokes-Darcy Model for Coupling Fluid Flow with Porous Media Flow
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TL;DR: Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid approach for solving multimodeling problems.
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Béatrice Rivière,Ivan Yotov +1 more
TL;DR: A locally conservative numerical method for solving the coupled Stokes and Darcy flows problem is formulated and analyzed and a discrete inf-sup condition and optimal error estimates are derived.