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首页> 外文期刊>Journal of Computational and Applied Mathematics >Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall
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Lie-group method for unsteady flows in a semi-infinite expanding or contracting pipe with injection or suction through a porous wall

机译：李群法在半无限膨胀或收缩管道中通过多孔壁进行注入或抽吸的非稳态流动

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The unsteady incompressible laminar flow in a semi-infinite porous circular pipe with injection or suction through the pipe wall whose radius varies with time is considered. The present analysis simulates the flow field by the burning of inner surface of cylindrical grain in a solid rocket motor, in which the burning surface regresses with time. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived [lbragimov, Elementary Lie Group Analysis and Ordinary Differential Equations, Wiley, New York, 1999; Hydon, Symmetry Methods for Differential Equations, Cambridge University Press, Cambridge, 2000; Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986; Seshadri, Na, Group invariance in engineering boundary value problems, Springer, New York, 1985; Yi, Fengxiang, Lie symmetries of mechanical systems with unilateral holonomic constraints, Chinese Sci. Bull. 45 (2000) 1354-1358; Moritz, Schwalm, Uherka, Finding Lie groups that reduce the order of discrete dynamical systems, J. Phys. A: Math. 31 (1998) 7379-7402; Nucci, Clarkson, The nonclassical method is more general than the direct method for symmetry reductions. An example of the Fitzhugh-Nagumo equation, Phys. Lett. A 164 (1992) 49-56; Basarab, Lahno, Group classification of nonlinear partial differential equations: a new approach to resolving the problem, Proceedings of Institute of Mathematics of NAS of Ukraine, vol. 43, 2002, pp. 86-92; Burde, Expanded Lie group transformations and similarity reductions of differential equations, Proceedings of Institute of Mathematics of NAS of Ukraine, vol. 43, 2002, pp. 93-101; Gandarias, Bruzon, Classical and nonclassical symmetries of a generalized Boussinesq equation, J. Nonlinear Math. Phys. 5 (1998) 8-12; Hill, Solution of Differential Equations by Means of One-Parameter Groups, Pitman Publishing Co., 1982]. The determining equations are a set of linear differential equations, the solution of which gives the transformation function or the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the cross-flow Reynolds number Re and the dimensionless wall expansion ratio a on velocity, flow streamlines, axial and radial pressure drop, and wall shear stress has been studied both analytically and numerically and the results are plotted. (c) 2006 Elsevier B.V. All rights reserved.
机译：考虑到半无限多孔圆管中的非稳态不可压缩层流，其通过管壁的注入或吸力，其半径随时间变化。本分析通过在固体火箭发动机中燃烧圆柱状颗粒的内表面来模拟流场，其中燃烧表面会随着时间而回归。我们应用李群方法确定偏微分方程的对称约简。 Lie-group方法从一组一般的无穷小变换开始，在这种变换下给定的偏微分方程是不变的，然后推导确定方程[lbragimov，基本李子群分析和常微分方程，Wiley，纽约，1999; Hydon，微分方程的对称方法，剑桥大学出版社，剑桥，2000;奥尔弗，《李群在微分方程上的应用》，施普林格，纽约，1986年。 Na，Seshadri，工程边界值问题的组不变性，纽约，Springer，1985;易凤祥，具有单边完整约束的机械系统的Lie对称性，中国科学。公牛。 45（2000）1354-1358;莫里茨，施瓦尔姆，乌赫尔卡，寻找减少离散动力系统的顺序的李群，物理。答：数学。 31（1998）7379-7402; Nucci，Clarkson，非对称方法比对称还原的直接方法更通用。 Fitzhugh-Nagumo方程的一个示例。来吧A 164（1992）49-56; Basarab，Lahno，非线性偏微分方程的组分类：一种解决该问题的新方法，乌克兰NAS的数学研究所会刊，第1卷。 2002年第43页，第86-92页;布尔德，扩展李群变换和微分方程的相似性约简，乌克兰国家科学与技术学院数学学报，第一卷。 2002年第43页，第93-101页; Gandarias，Bruzon，广义Boussinesq方程的古典和非古典对称性，J。非线性数学。物理5（1998）8-12; Hill，用单参数组求解微分方程，Pitman出版公司，1982年]。确定方程是一组线性微分方程，其解给出了转化函数或因变量和自变量的无穷小。在确定了组之后，可以从不变表面条件中找到给定偏微分方程的解，以使得其解导致相似变量，从而减少系统中自变量的数量。对横流雷诺数Re和无因次壁膨胀比α对速度，流线，轴向和径向压降以及壁切应力的影响进行了分析和数值研究，并绘制了结果。 （c）2006 Elsevier B.V.保留所有权利。

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