求解Navier-Stokes方程组的组合紧致迎风格式  

Combined Compact Upwind Difference Schemes for Navier-Stokes Equations

作　　者：梁贤[1,3] 田振夫[2,3] 

机构地区：[1]上海市应用数学和力学研究所,上海大学,上海200072 [2]复旦大学数学科学学院,上海200433 [3]宁夏大学数学计算机学院,宁厦银川750021

出　　处：《计算物理》2008年第6期659-667,共9页Chinese Journal of Computational Physics

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

摘　　要：给出一种新的至少有四阶精度的组合紧致迎风(CCU)格式,该格式有较高的逼近解率,利用该组合迎风格式,提出一种新的适合于在交错网格系统下求解Navier-Stokes方程组的高精度紧致差分投影算法.用组合紧致迎风格式离散对流项,粘性项、压力梯度项以及压力Poisson方程均采用四阶对称型紧致差分格式逼近,算法的整体精度不低于四阶.通过对Taylor涡列、对流占优扩散问题和双周期双剪切层流动问题的计算表明,该算法适合于对复杂流体流动问题的数值模拟.A fourth-order combined compact upwind （CCU） finite difference scheme with high resolving efficiency is proposed. A high-order compact difference algorithm for Navier-Stokes （NS） equations based on projection method is developed with CCU scheme on staggered grids. Convection terms are discretized by CCU scheme. Viscous terms, pressure gradient terms and pressure Poisson equations are discretized with fourth-order compact symmetric finite difference schemes. Numerical examples validate capability of the proposed approach. It is shown that the method is accurate and robust, and is applicable to complex fluid flows.

关 键 词：高精度 组合紧致迎风格式 投影法 数值模拟 

分 类 号：O351.2[理学—流体力学]