Application of the Adomian Decomposition Method to Oscillating Viscous Flows
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 121-132
Received: Jun. 3, 2016; Accepted: Jun. 13, 2016; Published: Jun. 29, 2016
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Chi-Min Liu, Division of Mathematics, General Education Center, Chienkuo Technology University, Changhua City, Taiwan
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In this paper three oscillating viscous flows are studied by applying the Adomian decomposition method (ADM). Major improvement is on the choice of the assignment of the first term of the decomposition series. Different from past studies in which the initial velocity profile of the whole domain is assigned as the first term of the decomposition series, the assignment in present study is simply the boundary velocity for Stokes’ second problem and the pressure gradient for pulsatile flows. This improvement demonstrates and implies that ADM is not only good in approaching the known exact solution, but also possesses the practicability in treating realistic problems. The derived approximate solutions accurate up to any order can be obtained after two key parameters are determined. Present results show an excellent agreement with those calculated by the exact solutions. Based on the present results, more periodic problems can be analyzed by ADM with the help of Fourier analysis.
Adomian Decomposition Method, Stokes’ Second Problem, Pulsatile Flow, Starting Assignment
To cite this article
Chi-Min Liu, Application of the Adomian Decomposition Method to Oscillating Viscous Flows, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 121-132. doi: 10.11648/j.acm.20160503.15
Copyright © 2016 Authors retain the copyright of this article.
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