Vorticity-pressure formulations for the Brinkman-Darcy coupled problem
Vorticity-pressure formulations for the Brinkman-Darcy coupled problem
复制标题
Brinkman-Darcy 耦合问题的涡量-压力公式
DOI：
10.1002/num.22312
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发表时间：
2018
影响因子：
3.9
通讯作者：
Anaya V
中科院分区：
文献类型：
--
作者：
Anaya V
我们引入了一个新的变分公式的Brinkman-Darcy方程制定的Brinkman涡度和全球压力。每个子域中的速度通过动量方程完全解耦，并且可以稍后从主要未知量恢复。还提出了一种新的有限元方法，包括等阶Nédélec和分段连续单元，分别用于涡量和压力。该方案的误差分析是在自然范数下进行的，其界限与流体粘度无关。一个适当的修改制定和分析允许我们指定的演示文稿的情况下，轴对称配置。我们提供了一组数值例子说明了所提出的离散化的鲁棒性，精度和效率。
We introduce a new variational formulation for the Brinkman‐Darcy equations formulated in terms of the scaled Brinkman vorticity and the global pressure. The velocities in each subdomain are fully decoupled through the momentum equations, and can be later recovered from the principal unknowns. A new finite element method is also proposed, consisting in equal‐order Nédélec and piecewise continuous elements, for vorticity and pressure, respectively. The error analysis for the scheme is carried out in the natural norms, with bounds independent of the fluid viscosity. An adequate modification of the formulation and analysis permits us to specify the presentation to the case of axisymmetric configurations. We provide a set of numerical examples illustrating the robustness, accuracy, and efficiency of the proposed discretization.