用格子Boltzmann方法构建大气动力学模式的初步研究

文中建立了一个格子Boltzmann模型 ,经过Chapman Enskog展开得到的方程组能完整描述正压大气的动力过程 ,成功地模拟了正压地转适应过程 ,对Obukhov的经典例子进行了数值检验。结果表明 ,Obukhov的结果只体现了科氏力和气压梯度力的平衡 ,而本模型可以精确地描述科氏力、惯性力和气压梯度力三者的完整平衡 ,与Obukhov线性理论相比 ,气压变化量的数值相差 2 8% ,说明了线性适应理论只在定性方面正确 ,在定量方面还不准确。数值结果还表明粘性力在地转适应过程中基本不起作用。同时 ,还模拟了一个更大尺度的适应问题 ,验证了气压场与风场适应过程取决于尺度大小这一论断数值试验表明 ,格子Boltzmann方法用于模拟大气运动是可行的 ,而且因其编程简洁方便 ,天然具有极好的并行性能 ,对于建立模拟大气和海洋这样涉及复杂动力热力过程的多相大规模数值模式很有发展潜力

A PRELIMINARY STUDY ON THE CONSTRUCTION OF ATMOSPHERIC DYNAMIC MODELS WITH LATTICE BOLTZMANN METHOD

Lattice Boltzmann Method is a recently developed discrete dynamic modeling method, which uses simple movement of particles and collision regulation to simulate complex behaviors of nonlinear systems and has been applied in many fields of computational fluid dynamics. Owing to its Lagrangian nature and the basic physical features inherited from the Boltzmann equation, this method has many advantages such as high precision, clear physical pictures and easy implementation of microscopic mechanism. A lattice Boltzmann model is constructed in this paper. Through the Chapman-Enskog expansion, a set of equations are derived which can describe the full dynamics of barotropic atmosphere. The process of the geostropic adjustment of largescale barotropic motion is simulated successfully, and the classical example of Obukhov is tested numerically. It turns out that Obukhov's results only showed the balance between the Coriolis force and the pressure gradient force, and the model presented in this paper can describe the full balance between the Coriolis force, the centrifugal force and the pressure gradient force. The variation of pressure calculated is 28% lower than Obukhov's result, which shows that the linear theory is quantitatively incorrect. Is turns out that the effect of viscosity can be neglected in the process of the geostropic adjustment. An example of larger scale is simulated to verify the theoretical conclusion that the adjustment between the pressure field and the wind field is determined by the scale considered. Numerical experiments showed that the lattice Boltzmann method is valid to simulate the atmosphere motion. This method is easy for programming , naturally parallel, and has good prospects in the massive multi-phase simulation of atmosphere and ocean.