具有周期边界条件和不可压流动的二维斯托克斯方程的Fourier解
Fourier solution of two-dimensional Navier Stokes equation with periodic boundary conditions and incompressible flow
摘要：
用复傅立叶基矢量表示流体速度的x、y分量，得到了具有周期边界条件的二维斯托克斯方程的近似解。基向量的所选空间是有限的，以允许数值计算，但大小可变。比较所得到的近似解，因为它们随所选向量空间的大小而变化，从而允许外推到无限基向量空间。结果表明，这样的解决方案，与完整的基向量空间，这将给出精确解，将失败的某些初始速度配置时，初始速度和时间t超过一定的限制。
英文摘要：
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
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