基于粒子群和蚁群算法的边界层微分方程求解

沿竖壁自然对流边界层微分方程组速度和温度均耦合,在打靶法中应用Newton求根的方法解对应的相似性微分方程组时对初值选择要求较高,在根值附近收敛变慢.将微分方程边值问题转化为初值问题求解的打靶过程可看作优化设计问题,用优化设计算法求解.将基于生物群信息传递规则和觅食规则提出的粒子群算法和蚁群算法应用到打靶法的求解过程中,并与其它优化算法计算结果进行了比较.结果表明,粒子群算法和蚁群算法用于沿变壁温竖壁自然对流层流边界层微分方程求解是可行的,计算过程稳定,对初值选择不敏感.

Boundary Layer Differential Equation Solution Based on Particle Swarm Optimization and Ant Colony Algorithm

The velocity and temperature are both coupled in natural convection boundary layer equations for fluid flow along vertical plate,the solution is sensitive to initial values when applying Newton root finding method to shooting method to solve corresponding similarity ordinary differential equations,and the convergence rate becomes slower when solutions are near roots.Ordinary differential equation boundary value problem is often solved with shooting method by transforming the problem into initial value problem,and the shooting process can be regarded as optimization problem.Particle swarm optimization algorithm and ant colony algorithm base on rules of information transmission and food hunting within biologic group are used in shooting process to solve natural convection boundary layer similarity equations with varied wall temperature and the results are compared with those obtained with other optimization algorithm.It is feasible to use particle swarm optimization algorithm and ant colony algorithm in solving natural convection boundary layer similarity equations,the calculation process is stable and the solution is not sensitive to initial values selection.