A 3D pseudospectral algorithm for fluid flows with permeable walls. Application to filtration
A 3D pseudospectral algorithm for fluid flows with permeable walls. Application to filtration
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用于具有渗透壁的流体流动的 3D 伪谱算法。
DOI：
10.1016/j.compfluid.2014.01.003
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发表时间：
2014
影响因子：
2.8
通讯作者：
Richard M. Lueptow
中科院分区：
文献类型：
--
作者：
N. Tilton;E. Serre;D. Martinand;Richard M. Lueptow
本文提出了一种Chebyshev配置Fourier-Galerkin拟谱方法，用于模拟圆柱形几何形状中的非定常三维流体流动，其中压力驱动流动通过可渗透边界。这样的系统出现在不同的应用中，并且由于通过达西定律在可渗透壁上的附加速度-压力耦合而难以模拟。本文推广了Raspo等人（2002）的投影方法，以保证达西定律的精确满足。一个多域求解器允许有效地处理开放的边界条件，需要渗透性缓冲区和海绵层。该方法是频谱收敛的，我们证明了压力预测是必要的，以获得二阶时间精度。通过模拟Taylor-Couette单元中的旋转过滤中的亚临界和超临界流动，证明了该方法模拟复杂物理系统的能力。对于亚临界的情况下，数值计算结果与解析解显示出良好的一致性。对于超临界的情况下，数值方法准确地解决了对流和绝对不稳定的流动与旅行的环形和螺旋涡结构，在良好的协议与当地的线性稳定性分析和实验观察。
The present work proposes a Chebyshev-collocation Fourier–Galerkin pseudospectral method for simulating unsteady, three-dimensional, fluid flows in cylindrical geometries with pressure-driven flow through permeable boundaries. Such systems occur in diverse applications and are challenging to simulate due to an additional velocity-pressure coupling on the permeable walls through Darcy’s law. The present work extends the projection method of Raspo et al. (2002) to assure Darcy’s law is satisfied exactly. A multidomain solver allows the efficient treatment of open boundary conditions that necessitate permeability buffers and a sponge layer. The method is spectrally convergent, and we demonstrate that pressure-prediction is necessary to obtain second-order temporal accuracy. The ability of the method to simulate complicated physical systems is demonstrated by simulating subcritical and supercritical flows in rotating filtration in Taylor–Couette cells. For subcritical cases, numerical results show excellent agreement with analytical solutions. For supercritical cases, the numerical method accurately resolves convectively and absolutely unstable flows with traveling toroidal and helical vortical structures that are in good agreement with a local linear stability analysis and experimental observations.