A SPECTRAL ELEMENT METHOD FOR FLUID-DYNAMICS - LAMINAR-FLOW IN A CHANNEL EXPANSION
A SPECTRAL ELEMENT METHOD FOR FLUID-DYNAMICS - LAMINAR-FLOW IN A CHANNEL EXPANSION
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DOI：
10.1016/0021-9991(84)90128-1
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发表时间：
1984-01-01
影响因子：
4.1
通讯作者：
PATERA, AT
中科院分区：
文献类型：
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作者：
PATERA, AT
结合有限元方法的通用性和谱技术的精度，提出了一种数值求解不可压N-S方程的谱单元方法。在谱单元离散化中，将计算区域分解为一系列单元，每个单元中的速度通过切比雪夫配置点表示为高阶拉格朗日插值项。控制方程的双曲段用显式配置格式处理，而压力和粘性贡献用由变分原理导出的投影算子隐式处理。在一维流入-流出平流-扩散方程上演示了该方法的实现，然后将该方法应用于通道扩展中的层流二维(分离)流动。并与实验和前人的数值计算结果进行了比较。
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.