高精度气体动理学格式与湍流模拟

High-order accurate gas-kinetic scheme and turbulence simulation

本文介绍了多维高阶精度气体动理学格式的构造原理及其在可压缩湍流直接数值模拟中的初步应用.通过对初始分布函数和平衡态分布的多维高阶展开,利用BGK方程的通解可以得到单元界面上随时间演化的分布函数,从而建立具有真正多维特性的高阶精度气体动理学有限体积格式.应用建立的格式对可压缩各向同性衰减湍流和槽道湍流进行了数值模拟,得到的流场结果与已有研究相吻合.研究表明,相比于已有二阶气体动理学方法,高阶动理学格式具有更高的求解精度.

The multidimensional high-order accurate gas-kinetic scheme is introduced and preliminarily applied into the direct numerical simulation of compressible turbulence. Based on the high-order multidimensional expansion of the initial and equilibrium distribution functions, the time-dependent distribution function at a cell interface can be obtained with the integral solution of BGK equation. Then the high-order accurate gas-kinetic finite-volume scheme can be developed with truly multidimensional characteristics. The new scheme is applied into the numerical simulation of decaying homogeneous isotropic turbulence and compressible channel flow, and the predicted flow fields agree well with existing studies. It is shown that when compared to the second-order gas-kinetic scheme, the high-order scheme possesses better accuracy.