Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations
Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations
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DOI：
10.1002/sapm1971504293
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发表时间：
1971-12
影响因子：
2.7
通讯作者：
S. Orszag
中科院分区：
文献类型：
--
作者：
S. Orszag
用Galerkin(谱)方法对简单边界内的不可压缩流动进行了数值模拟。本文的主要内容是发展变换方法来有效地模拟具有周期和自由滑移边界条件的箱形几何结构中的流动。对于Taylor-Green涡旋，说明了将已知的对称性和不变性结合到变换方法中的技术。文中还解释了用Galerkin方法精确有效地表示刚性无滑移边界条件的方法。为了处理更复杂的几何结构中更复杂的动力学相互作用，引入了一类拟谱近似。本系列后面的论文将展示谱方法相对于有限差分方法在模拟当前感兴趣的许多流动方面的重要优势，并将针对不同的过渡和湍流给出具体的数值结果。
Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries. A major part of the paper is devoted to the development of transform methods for efficient simulation of flows in box geometries with periodic and free-slip boundary conditions. Techniques for incorporating known symmetries and invariances into transform methods are illustrated for the Taylor-Green vortex. Galerkin methods for accurate and efficient representation of rigid no-slip boundary conditions are also explained. A class of pseudospectral approximations is introduced in order to handle more complicated dynamical interactions in more complicated geometries. Later papers in this series will demonstrate the important advantages of spectral methods over finite-difference methods for simulation of many of the flows of current interest and will present specific numerical results for various transition and turbulent flows.