J. Amorocho Hydraulics Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA.
Hydrologic Research Laboratory and J. Amorocho Hydraulics Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA.
Sci Rep. 2017 Jul 25;7(1):6416. doi: 10.1038/s41598-017-06669-z.
Scaling conditions to achieve self-similar solutions of 3-Dimensional (3D) Reynolds-Averaged Navier-Stokes Equations, as an initial and boundary value problem, are obtained by utilizing Lie Group of Point Scaling Transformations. By means of an open-source Navier-Stokes solver and the derived self-similarity conditions, we demonstrated self-similarity within the time variation of flow dynamics for a rigid-lid cavity problem under both up-scaled and down-scaled domains. The strength of the proposed approach lies in its ability to consider the underlying flow dynamics through not only from the governing equations under consideration but also from the initial and boundary conditions, hence allowing to obtain perfect self-similarity in different time and space scales. The proposed methodology can be a valuable tool in obtaining self-similar flow dynamics under preferred level of detail, which can be represented by initial and boundary value problems under specific assumptions.
通过利用点尺度变换李群，获得了三维（3D）雷诺平均纳维-斯托克斯方程作为初始和边界值问题的自相似解的尺度条件。利用开源纳维-斯托克斯求解器和推导出的自相似性条件，我们展示了在刚性盖腔问题的流动动力学时间变化下，在放大和缩小域内的自相似性。所提出方法的优势在于，它不仅可以通过考虑控制方程，还可以通过初始和边界条件来考虑潜在的流动动力学，从而可以在不同的时间和空间尺度上获得完美的自相似性。该方法可以成为在特定假设下通过初始和边界值问题来获得所需细节水平下自相似流动动力学的有用工具。
