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 - <p style="text-align: justify;">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 ${\bf u}\cdot {\bf n}_f&gt;0$ (not hold for general case but still in many situation, such as the gentle river). Under a modest time step restriction of the form $\Delta&nbsp; t\leq C$, 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.</p>