Rehm Ronald G, Baum Howard R, Barnett P Darcy
National Bureau of Standards, Washington, DC 20234.
J Res Natl Bur Stand (1977). 1982 Mar-Apr;87(2):165-185. doi: 10.6028/jres.087.013.
Model equations describing large scale buoyant convection in an enclosure are formulated with the vorticity and stream function as dependent variahles. The mathematical model, based on earlier work of the authors, is unique in two respects. First, it neglects viscous and thermal conductivity effects. Second the fluid is taken to be thermally expandable: large density variations are allowed while acoustic waves are filtered out. A volumetric heat source of specified spatial and temporal variation drives the flow in a two-dimensional rectangular enclosure. An algorithm for solution of the equations in this vorlicily, stream-function formulation is presented. Results of computations using this algorithm are presented. Comparison of these results with those obtained earlier by the authors using a finite difference code to integrate the primitive equations show excellent agreement. A method for periodically smoothing the computational results during a calculation, using Lanczos smoothing, is also presented. Computations with smoothing at different time intervals are presented and discussed.
以涡度和流函数作为因变量，建立了描述封闭腔内大规模浮力对流的模型方程。该数学模型基于作者早期的工作，在两个方面具有独特性。首先，它忽略了粘性和热传导效应。其次，流体被视为可热膨胀的：允许有较大的密度变化，同时滤除声波。一个具有特定空间和时间变化的体积热源驱动二维矩形封闭腔内的流动。提出了一种求解该涡度、流函数形式方程的算法。给出了使用该算法的计算结果。将这些结果与作者早期使用有限差分代码对原始方程进行积分得到的结果进行比较，显示出极好的一致性。还提出了一种在计算过程中使用兰佐斯平滑对计算结果进行周期性平滑的方法。给出并讨论了在不同时间间隔进行平滑处理的计算结果。
