Volume 11, Issue 2
Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions

Adv. Appl. Math. Mech., 11 (2019), pp. 381-405.

Published online: 2019-01

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• 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.

• Keywords

Fully evolutionary Navier-Stokes/Darcy problem, partitioned time stepping method, Beavers-Joseph-Saffman, interface conditions, error estimate.

65M55, 65M70

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@Article{AAMM-11-381, author = {Jia , HongenZhang , Yusha and Yu , Jiaping}, title = {Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {2}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0102}, url = {http://global-sci.org/intro/article_detail/aamm/12968.html} }
TY - JOUR T1 - Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions AU - Jia , Hongen AU - Zhang , Yusha AU - Yu , Jiaping JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 381 EP - 405 PY - 2019 DA - 2019/01 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0102 UR - https://global-sci.org/intro/article_detail/aamm/12968.html KW - Fully evolutionary Navier-Stokes/Darcy problem, partitioned time stepping method, Beavers-Joseph-Saffman, interface conditions, error estimate. AB -

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.

Hongen Jia, Yusha Zhang & Jiaping Yu. (2020). Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions. Advances in Applied Mathematics and Mechanics. 11 (2). 381-405. doi:10.4208/aamm.OA-2018-0102
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