封闭方腔内自然对流问题的高精度紧致差分格式  

High-accuracy compact difference format for natural convection problems in enclosed square cavity

作　　者：金涛[1,2] 马廷福[1,2] 葛永斌[2] 

机构地区：[1]中国矿业大学银川学院,宁夏银川750011 [2]宁夏大学应用数学与力学研究所,宁夏银川750021

出　　处：《兰州理工大学学报》2013年第5期139-144,共6页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10502026;10662006);宁夏高等学校科学技术研究项目

摘　　要：提出数值求解二维非定常不可压涡量-流函数Navier-Stokes/Boussinesq方程组的高精度紧致差分格式,格式空间为四阶精度,时间为二阶精度,并且是无条件稳定的.为了验证高精度紧致差分格式的精确性和可靠性,对有解析解的二维非定常不可压Navier-Stokes/Boussinesq方程组的Dirichlet问题和典型的封闭方腔自然对流问题进行数值模拟.A high-accuracy compact difference format of Navier-Stokes/Boussinesq equation set was proposed to solve numerically the two-dimensional non-stationary incompressible vorticity-stream function. This format was of fourth-order accuracy in spaces, second-order accuracy in time, and unconditionally stable. In order to prove the accuracy and reliability of the high-accuracy compact difference format presented in this paper, some numerical simulation of the two-dimensional non-stationary incompressible NavierStokes/Boussinesq equations with Dirichlet boundary conditions, which have analytical solution, and the typical problem of natural-convection in enclosed square cavity were conducted.

关 键 词：不可压Navier-Stokes BOUSSINESQ方程组 涡量-流函数方法 高阶紧致差分格式 自然对流 

分 类 号：O241.82[理学—计算数学]