基于同位网格的一种新的定压边界处理方法

摘要

The idea of SIMPLE-P algorithm dealing with pressure boundary was extended to collocated grid system. The pressure equation of boundary control volume was reconstructed in consideration of the mathematical characters of the pressure and velocity boundary conditions. The solving steps of flow and heat transfer problem in specified pressure boundary conditions were discussed based on the IDEAL algorithm dealing with pressure and velocity coupling. The methods were evaluated by Kovasznay flow, pressure-driven laminar internal flow and buoyancy-driven flow, and the solutions were compared with those obtained from the literature and experiment. The results show that the proposed method is accurate and efficient. For the specified pressure boundary problem, it has better convergence performance than SIMPLE-P algorithm. Especially for the problem of natural convection in large-space, the good accuracy solutions can be obtained by the new method with a relatively small domain, which can save large number of storage space and computing time.%将SIMPLE-P算法中处理压力边界的思想推广到同位网格中,综合考虑压力和速度边界条件的数学特性,重新推导边界控制体的压力方程,借鉴IDEAL算法处理压力和速度耦合的思想,讨论定压边界流动传热问题的求解步骤.通过Kovasznay流、压力驱圆管层流和浮力驱动流等几个典型算例对新方法和SIMPLE-P算法进行考核并将计算结果与文献中的数值解和实验值进行对比.结果表明:新方法是准确有效的,对于定压边界问题的求解较之SIM-PLE-P算法具有更好的收敛性能;对于大空间自然对流问题使用新方法在较小的计算区域就可获得高精度的结果,从而节省了大量的存储空间和运算时间.