Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations
Orthogonal spline collocation methods for the stream function-vorticity formulation of the Navier-Stokes equations
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DOI：
10.1002/num.20269
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发表时间：
2008-03-01
影响因子：
3.9
通讯作者：
Sun, Weiwei
中科院分区：
文献类型：
--
作者：
Fairweather, Graeme;Ma, Heping;Sun, Weiwei
本文提出了一种正交样条配置空间离散方法，用于求解二维Navier-Stokes方程的流函数-涡量完全耦合格式。对于时间步进，采用了三层蛙跳格式。这种方法是代数线性的，并且在每个时间步，产生一个系统的线性方程组的形式所产生的OSC近似的双调和Dirichlet问题，可以解决一个快速的直接方法。对于半离散方法和全离散的蛙跳格式，给出了在空间上H-1模的误差估计，l = 1，2，在时间上也具有二阶精度.数值结果证实了理论分析，并表现出超收敛现象，提供超收敛近似的速度分量。(c)约翰威利父子公司(c)2007 Wiley Periodicals，Inc.
An orthogonal spline collocation (OSC) spatial discretization is proposed for the solution of the fully coupled stream function-vorticity formulation of the Navier-Stokes equations in two dimensions. For the time-stepping, a three-level leapfrog scheme is employed. This method is algebraically linear, and, at each time step, gives rise to a system of linear equations of the form arising in the OSC approximation of the biharmonic Dirichlet problem and can be solved by a fast direct method. Error estimates in the H-1-norm in space, l = 1, 2, are derived for the semi-discrete method and the fully-discrete leapfrog scheme which is also shown to be second order accurate in time. Numerical results are presented which confirm the theoretical analysis and exhibit superconvergence phenomena, which provide superconvergent approximations to the components of the velocity. (c) John Wiley & Sons, Inc. (c) 2007 Wiley Periodicals, Inc.