A domain decomposition method for the time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition
A domain decomposition method for the time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition
复制标题
具有Beavers-Joseph界面条件和缺陷边界条件的时变Navier-Stokes-Darcy模型的域分解方法
DOI：
10.1016/j.jcp.2020.109400
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发表时间：
2020-06
影响因子：
4.1
通讯作者：
Lin Yanping
中科院分区：
文献类型：
--
作者：
Qiu Changxin;He Xiaoming;Li Jian;Lin Yanping
本文提出了一种求解具有beaver - joseph界面条件和缺陷边界条件的时变Navier-Stokes-Darcy模型的区域分解方法。通过直接重组包括beaver - joseph条件在内的三个界面条件中的项，构建了Navier-Stokes域和Darcy域之间的Robin边界条件。为了避免传统的域分解方法在每个时间步长都需要迭代，根据前一时间步长的数值解直接预测当前时间步长Robin型传输条件所需的接口信息。首先采用后向欧拉格式进行时间离散，然后采用有限元方法进行空间离散。对于具有beaver - joseph界面条件的时相关Navier-Stokes-Darcy模型，严格分析了该区域分解方法的收敛性。分析中的主要困难来自非线性项和bevers - joseph界面条件，包括用于完全离散化分析的离散Gronwall不等式的一系列技术处理和最终特殊范数。在上述准备的基础上，我们进一步发展了在区域分解方法框架下的拉格朗日乘子方法，以克服边界条件缺陷引起的非唯一解的困难。本文一个有趣的发现是拉格朗日乘子是随时间变化的函数而不是常数。为了提高时间离散化的精度阶数，采用三步后向微分格式代替后向欧拉格式。与第一种方案相比，第二种方案允许我们使用相对较大的时间步长来减少计算成本，同时保持相同的精度。数值算例说明了该方法的特点。
In this article a domain decomposition method is proposed to solve a time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition. Robin boundary conditions between the Navier-Stokes domain and Darcy domain are constructed by directly re-organizing the terms in the three interface conditions, including the Beavers-Joseph condition. In order to avoid the traditional iteration for the domain decomposition method at each time step, the interface information, which is needed for the Robin type transmission conditions at the current time step, is directly predicted based on the numerical solution of the previous time steps. Backward Euler scheme is first utilized for the temporal discretization while finite elements are used for the spatial discretization. The convergences of this domain decomposition method are rigorously analyzed for the time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition. The major difficulties in the analysis arise from nonlinear terms and Beavers-Joseph interface condition, including a series of technical treatments and the final special norm used in the discrete Gronwall's inequality for the analysis of full discretization. Based on the above preparation, we further develop a Lagrange multiplier method under the framework of the domain decomposition method to overcome the difficulty of non-unique solutions arising from the defective boundary condition. One interesting finding of this paper is that the Lagrange multipliers are time dependent functions instead of constants. In order to improve the accuracy order for the temporal discretization, a three-step backward differentiation scheme is used to replace the backward Euler scheme. Compared with the first scheme, the second one allows us to use the relative larger time step to reduce the computational cost while keeping the same accuracy. Numerical examples are provided to illustrate the features of the proposed method.
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影响因子：
1.7
作者：
M. Hadji;A. Assala;F. Z. Nouri
通讯作者：
M. Hadji;A. Assala;F. Z. Nouri
DOI：
--
发表时间：
2007
期刊：
--
影响因子：
--
作者：
V. Ervin;E. Jenkins;S. Sun
通讯作者：
V. Ervin;E. Jenkins;S. Sun
DOI：
10.1007/978-3-319-40361-8_1
发表时间：
2015-05
期刊：
ArXiv
影响因子：
--
作者：
E. Fattahi;C. Waluga;B. Wohlmuth;U. Rüde
通讯作者：
E. Fattahi;C. Waluga;B. Wohlmuth;U. Rüde
一种高效、长时间准确的Stokes-Darcy系统三阶算法
影响因子：
2.1
作者：
Chen Wenbin;Gunzburger Max;Sun Dong;Wang Xiaoming;Wang XM
通讯作者：
Wang XM
影响因子：
4.1
作者：
O. Rokovs;J. Zeman;Milan Jir'asek
通讯作者：
O. Rokovs;J. Zeman;Milan Jir'asek