论文标题

多孔夹杂物的流体流动流量降低技术还原技术

Multiscale model reduction technique for fluid flows with heterogeneous porous inclusions

论文作者

Vasilyeva, Maria, Mallikarjunaiah, S. M., Palaniappan, D.

论文摘要

考虑了循环多孔夹杂物和周围二维粘性流体流量问题的数值处理。数学模型由自由流域中的Navier-Stokes方程$ω_f$和非线性对流Darcy-Brinkman-Forchheimer方程$ω_p$描述。众所周知,这种异质域中问题的数值解需要一个非常细的计算网格,该网格可以在网格水平上解决包含物。相关系统的尺寸变化需要减少模型技术。在这里,我们提出了一种基于广义多尺度有限元方法(GMSFEM)的多尺度模型还原技术。我们讨论了基于有或没有过度采样策略的本地问题的解决方案的解决方案的速度领域的多尺度基础功能的构建。考虑了三个测试用例,用于给定三个关键模型参数的给定选择,即雷诺数($ re $),forchheimer系数($ c $)和darcy号($ da $)。对于测试运行,雷诺数值值为$ re = 1、10、100 $,而forchheimer系数和darcy编号分别为$ c = 1、10 $和$ da = 10^{ - 5},10^{ - 4},10^{ - 4},10^{ - 3} $。当我们增加每个域中的多尺度函数的数量时,我们可以从数值上研究该方法的收敛性,并观察到多尺度方法的良好性能。

Numerical treatment of the problem of two-dimensional viscous fluid flow in and around circular porous inclusions is considered. The mathematical model is described by Navier-Stokes equation in the free flow domain $Ω_f$ and nonlinear convective Darcy-Brinkman-Forchheimer equations in porous subdomains $Ω_p$. It is well-known that numerical solutions of the problems in such heterogeneous domains require a very fine computational mesh that resolve inclusions on the grid level. The size alteration of the relevant system requires model reduction techniques. Here, we present a multiscale model reduction technique based on the Generalized Multiscale Finite Element Method (GMsFEM). We discuss construction of the multiscale basis functions for the velocity fields based on the solution of the local problems with and without oversampling strategy. Three test cases are considered for a given choice of the three key model parameters, namely, the Reynolds number ($Re$), the Forchheimer coefficient ($C$) and the Darcy number ($Da$). For the test runs, the Reynolds number values are taken to be $Re = 1, 10, 100$ while the Forchheimer coefficient and Darcy number are chosen as $C= 1, 10$ and $Da = 10^{-5}, 10^{-4}, 10^{-3}$, respectively. We numerically study the convergence of the method as we increase the number of multiscale basis functions in each domain, and observe good performance of the multiscale method.

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