胀缩渗透圆形管道内多解的构造
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摘要
多解存在于胀缩渗透圆形管道内的流体流动问题中。基于奇异摄动方法,给出了关于多解的渐近解。数值解与渐近解进行了比较,结果表明数值解与渐近解吻合的很好,说明所构造的渐近解是可靠且有效的。这样不仅可以利用此渐近解去拓展基于血液流的胀缩渗透圆形管道内的研究,而且也丰富了对多解的认识,有助于掌握血液在血管内的流动规律,对治疗心脑血管等病具有重要的借鉴意义。
Multiple solutions exist in laminar flow arising from a porous pipe with expanding or contracting wall. Based on a singular perturbation method,asymptotic solutions are obtained.Asymptotic solutions agree well with numerical solutions,indicating that the asymptotic solutions are efficient.It not only provides how to construct multiple solutions,but also illustrates the corresponding mechanism,which is helpful to understand the current problems.
Multiple solutions exist in laminar flow arising from a porous pipe with expanding or contracting wall. Based on a singular perturbation method,asymptotic solutions are obtained.Asymptotic solutions agree well with numerical solutions,indicating that the asymptotic solutions are efficient.It not only provides how to construct multiple solutions,but also illustrates the corresponding mechanism,which is helpful to understand the current problems.
引文
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[10]张伟江,周明儒,林武忠,等.奇异摄动导论[M].北京:科学出版社,2012:68-95.
[2]LI L,ZHANG H,LIN P.Asymptotic solutions for laminar flow based on blood circulation through a uniformly porous channel with retractable walls and an applied transverse magnetic field[J]. Powder technology,2017,308(2):398-409.
[3]SI X H,LI L,ZHENG L C.The exterior unsteady viscous flow and heat transfer due to a porous expanding stretching cylinder[J].Computers&fluids,2014,105(1):280-284.
[4]吴望一.流体力学[M].北京:北京大学出版社,2004:112-120.
[5]陈懋章.粘性流体力学基础[M].北京:高等教育出版社,2009:156-171.
[6]UCHIDA S,AOKI H.Unsteady flows in a semi-infinite contracting or expanding pipe[J].Journal of fluid mechanics,1977,82(2):371-387.
[7]TERRILL R M.Laminar flow in a uniformly porous channel[J].Aeronautical journal,1957,15(11):15-20.
[8]TERRILL R M,SHRESTHA G M.Laminar flow through channels with porous walls and with an applied transverse magnetic field[J]. Applied scientific research,1964,11(2):134-144.
[9]TERRILL R M,SHRESTHA G M.Laminar flow through a channel with uniformly porous walls of different permeability[J]. Applied scientific research,1966,15(1):440-468.
[10]张伟江,周明儒,林武忠,等.奇异摄动导论[M].北京:科学出版社,2012:68-95.