Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions
Year: 2019
Author: Hongen Jia, Yusha Zhang, Jiaping Yu
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 381–405
Abstract
In this report, a partitioned time stepping algorithm for Navier Stokes/Darcy model is analyzed. This method requires only solving one, uncoupled Navier Stokes and Darcy problems in two different sub-domains respectively per time step. On the interface, the simplified Beavers-Joseph-Saffman conditions are imposed with an additional assumption ${\bf u}\cdot {\bf n}_f>0$ (not hold for general case but still in many situation, such as the gentle river). Under a modest time step restriction of the form $\Delta t\leq C$, where $C=C$ (physical parameters), we prove stability of the method and get the error estimates. Numerical tests illustrate the validity of the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0102
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 381–405
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Fully evolutionary Navier-Stokes/Darcy problem partitioned time stepping method Beavers-Joseph-Saffman interface conditions error estimate.