Abstract
While computational methods for solving Stokes-flow problems have existed for some time, these have depended on specialized codes developed specifically, for this type of problem. This work shows how to combine traditional applied mathematics and a modern over-the-counter software package Matlab to solve and study Stokes flow in a channel with a splitter plate. Specifically exact unidirectional flow solutions are used as a basis for choosing boundary conditions for Matlab to anticipate the boundary conditions of a Stokes flow. A method for selecting zeroth and first-order approximate boundary conditions is presented, along with a suggestion for finding a second-order approximation. It is also shown that small errors made in choosing the approximate boundary conditions do not grow as one moves away from the boundary into the interior of the flow. Finally several computational examples using this approach are presented.
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References
C.V. Camp and G.S. Gipson, Boundary Element Analysis of Nonhomogeneous Biharmonic Phenomena. Berlin: Springer-Verlag (1992) 246 pp.
P.J. Roache, Computational Fluid Dynamics. Albuquerque: Hermosa Publishers (1985) 446 pp.
A.R. Mitchell and D.F. Griffiths, The Finite Difference Method in Partial Differential Equations. Chichester: Wiley (1980) 272 pp.
V.T. Buchwald, Eigenfunctions of plane elastostatics I. The strip. Proc. R. Soc. London A 277 (1964) 385–400.
R.C.T. Smith, The bending of a semi-infinite strip. Aust. J. Sci. Res. 5 (1952) 227–237.
D.A. Spence, A class of biharmonic end-strip problems arising in elasticity and Stokes flow. IMA J. Appl. Math. 30 (1983) 107–139.
T.N. Phillips, Singular matched eigenfunction expansions for Stokes flow around a corner. IMA J. Appl. Math. 42(1989) 13–26.
S.A. Trogdon and D.D. Joseph, Matched eigenfunction expansions for slow flow over a slot. J. Non-Newtonian Fluid Mech. 10 (1982) 185–213.
V.V. Meleshko, Steady Stokes flow in a rectangular cavity. Proc. R. Soc. London A 452 (1996) 1999–2022.
D.H. Michael and M.E. O’Neill, The separation of Stokes flows. J. Fluid Mech. 80 (1977) 785–794.
B. Noble, Methods Based on the Wiener-Hopf Technique. 2nd. ed. New York: Chelsea Press (1988) 246 pp.
I.D. Abrahams, On the solution of Wiener-Hopf problems involving non-commutative matrix kernel decompositions. SIAM J. Appl. Math. 57 (1997) 541–567.
I.D. Abrahams and A.M.J. Davis, Asymmetric channel divider and the Stokes entry problem, in preparation.
G.B. Folland, Introduction to Partial Differential Equations. Princeton: Princeton University. Press (1976) 349 pp.
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© 2001 Springer Science+Business Media Dordrecht
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Davis, A.M.J., Fehribach, J.D. (2001). Stokes flow around an asymmetric channel divider; a computational approach using Matlab . In: Kuiken, H.K. (eds) Practical Asymptotics. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0698-9_11
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DOI: https://doi.org/10.1007/978-94-010-0698-9_11
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