二维Navier-Stokes方程流函数形式的二阶隐的Legendre谱格式

Second Order Implicit Legendre Spectrum Approximation of Two-Dimensional Navier-Stokes Equations in Stream Function

考虑了Navier-Stokes方程流函数形式的初边值问题。引入了三线性算子,然后介绍了这个问题的弱形式。针对二维Navier-Stokes方程建立了高精度的二阶隐的Legendre谱格式,该格式在时间方向具有二阶精度,在空间方向具有谱精度,且保持了离散能量的守恒性。此外,还模拟了该问题长时间性态。

The initial-boundary value problem of the Navier-Stokes equations in stream function form was considered. A trilinear form was introduced to deal with the nonlinear term. A weak formulation of this problem was provided. For two-dimensional Navier-Stokes equation, the second order implicit legendre approximation with high-accuracy was established. This approximation has two order accuracy in time direction ,and spectral accuracy in space direction, and keeps the conservation of the dispersed energy. The long-term behavior of the Navier-Stokes equations in stream function form was simulated.