小波自适应方法模拟二维涡旋演化

以涡量方程为控制方程,模拟初始状态涡量分布为高斯分布三个涡旋演化过程.提出一个关联实际流动的小波系数临界值,小波系数分为临界值以上及以下部分,进而涡量可分成尺度系数项、小波系数突出项和小波系数平凡项三部分.只采用尺度系数项和小波系数突出项近似涡量,既可以节约计算量,还可以自动追踪绝大部分的拟涡能.数值结果表明,用不到10%的小波系数,可控制99%以上的拟涡能.

Numerical Simulation of Two-dimensional Vortexes with Adaptive Wavelet Method

Taking vorticity equation as a controlling equation, we simulate three vortexes developing progress with initial condition of Gaussian probability vorticity distribution. The wavelet expression of vorticity contains scaling coefficient term and wavelet coefficient tenn. The latter can be divided into a significant wavelet coefficient term and a trivial wavelet coefficient term reference to a given critical value. The critical value contains practical flow information. The vorticity is reconstructed only with scaling coefficients and significant wavelet coefficients. It saves computing time and capture most part of entrophy. Numerical results show that scaling coefficients together with significant wavelet coefficients is less than 10% of total wavelet coefficients, but they contains more than 99% of total enstrophy.