通过求解输运方程计算壁面距离  

Computations of Wall Distances by Solving a Transport Equation

作　　者：徐晶磊[1] 阎超[1] 范晶晶[1] 

机构地区：[1]北京航空航天大学国家计算流体力学实验室,北京100191

出　　处：《应用数学和力学》2011年第2期135-143,共9页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划资助项目(2009CB724104);中国博士后科学基金资助项目(20090450285)

摘　　要：壁面距离在当代湍流模化中仍然扮演着关键角色,然而苦于遍历计算壁面距离的高昂代价,该文考虑了求解偏微分方程的途径.基于Eikonal方程构造出类Euler形式的输运方程,这样,可以直接利用求解Euler和Navier-Stokes方程的CFD程序使用的高效数值格式和部分代码.基于北航的MI-CFD(CFD for missles)数值平台,详尽地介绍了该输运方程在直角坐标下的求解过程.使用隐式LUSGS时间推进和迎风空间离散,发现该方程具有鲁棒快速的收敛特性.为了保证精度,网格度量系数必须也迎风插值计算.讨论了初始条件和边界条件的特殊处理.成功应用该壁面距离求解方法计算了几个含1-1对应网格和重叠网格的复杂外形.Motivated by the large expense to compute wall distances which still play a key role in modern turbulence modeling,the approach of solving partial differential equations is considered.An Euler-like transport equation was proposed based on Eikonal equation so that efficient algorithms and code components developed for solving transport equations such as Euler and Navier-Stokes can be reused.A detailed implementation of the transport equation in Cartesian Coordinates was provided based on code MI-CFD of BUAA.The transport equation was found to have robust and rapid convergence using implicit LUSGS time advancement and upwind spatial discretization.Geometric derivatives must also be upwind determined for accuracy assurance.Special treatments on initial and boundary conditions were discussed.This distance solving approach is successfully applied on several complex geometries with 1-1 blocking or -overset grids.

关 键 词：壁面距离 数值模拟 重叠网格 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]