Adv. Appl. Math. Mech., 11 (2019), pp. 381-405.
Published online: 2019-01
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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} }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.