Abstract：The brachistochrone problem with viscous friction was studied to optimize the beam window (BW) shape of an accelerator driven sub-critical system (ADS) target. A set of nonlinear integral equations was derived using the variational method. The Newton iteration method could not get a convergent solution or an approximate solution for the highly viscous conditions, so an optimization method was developed. The particle swarm optimization (PSO) algorithm was found to be more efficient for the highly viscous conditions than other three heuristic algorithms with approximately linear convergence. The flow separation is later and the stagnation region is smaller for the brachistochrone BW instead of the semielliptical BW, which enhances the heat transfer.
李胜强, 谭铭, 张展博. 含黏性力最速降线问题的最优化解法及其在ADS设计中的应用[J]. 清华大学学报（自然科学版）, 2018, 58(6): 563-569.
LI Shengqiang, TAN Ming, ZHANG Zhanbo. An optimization method of brachistochrone problem with viscous friction and its application in ADS design. Journal of Tsinghua University(Science and Technology), 2018, 58(6): 563-569.
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2018, Vol. 58 
