Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions

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.

Author Details

Hongen Jia

Yusha Zhang

Jiaping Yu

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