采用非结构网格的IDEAL算法实现及定压边界条件处理  

Implementation of IDEAL Algorithm in Unstructured Grids and Treatment of Specified Pressure Boundary Conditions

作　　者：王辉[1] 徐明海[1] 

机构地区：[1]中国石油大学(华东)储运与建筑工程学院,青岛266555

出　　处：《西安交通大学学报》2011年第5期23-30,共8页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(50376043);中央高校基本科研业务费专项资金资助项目(10CX05011A)

摘　　要：在非结构网格系统中采用有限容积法对不可压N-S方程进行了离散,其中对流项采用二阶迎风格式,扩散项采用超松弛校正格式.通过修正的动量插值格式构造了压力方程,利用IDEAL算法处理压力与速度的耦合.利用Taylor展式导出了邻近边界内节点的压力计算公式,进而将边界静压引入到压力方程的迭代计算中,确保了边界信息向内部区域的有效传递.根据质量守恒定律分别导出了压力入口和出口边界的速度计算公式,结合伯努利定律给出了总压边界的处理方法.通过压力驱动管内层流、三通管层流以及浮力驱动流等几个典型算例对文中方法进行了考核,并将计算结果与文献中的基准解和实验值进行了对比.结果表明,不管是静压边界还是总压边界,采用该处理方法均能获得令人满意的结果,尤其对于大空间自然对流问题,可以在保证精度的前提下节省大量的存储空间和运算时间.On the basis of the finite volume method,the incompressible N-S equation was discretized with the second order upwind scheme to evaluate the convective term and the over-relaxed correction approach to calculating the diffusion term in unstructured grids systems.The pressure equation was derived by the modified momentum interpolation method,and the IDEAL algorithm was adopted in unstructured grids to treat the coupling of pressure and velocity.The formula for calculating static pressure of the internal nodes near boundary was derived by the Taylor expansion,and then the boundary pressure was employed in the iterative computation of the pressure equation to ensure the transfer of information from boundary to internal domain.The calculation formulae of the velocity at the pressure inlet and outlet were derived from the mass conservation law.The method proposed was evaluated by pressure-driven laminar internal flow,T-branch flow and buoyancy-driven flow,and then the solutions were compared with those in the literature.The results show that the present method is effective and feasible.

关 键 词：定压边界 非结构网格 IDEAL算法 不可压缩流 有限容积法 

分 类 号：O357.1[理学—流体力学] TK124[理学—力学]