Abstract
A boundary integral equation formulation is used to model the stratified flow of two Newtonian viscous liquids, in which the geometrical detail of the interface between the layers is not known in advance. The technique is tested by comparing predictions with the results of previous finite element solutions, and found to perform well. Finally, the method is used to examine the two-layer jet theory of Tanner (1980) as a means of simplifying the modelling of complex extrudate swell problems.
Similar content being viewed by others
References
Banerjee, P. K.; Cathie, D. N. (1980): A direct formulation and numerical implementation of the boundary element method for two-dimensional problems of elastoplasticity. Int. J. Mech. Sci. 22, 233–245
Bialecki, R.; Nowak, A. J. (1981): Boundary value problems for non-linear material and non-linear boundary conditions. Appl. Math. Mod. 5, 417–421
Binding, D. M.; Walters, K.; Dheur, J.; Crochet, M. J. (1987): Interfacial effects in the flow of viscous and elasticoviscous liquids. Phil. Trans. R. Soc. Lond. A323, 449–469
Brebbia, C. A. (ed) (1988): Boundary elements X, vols. 1–4, Proc. of the 10th Int. Conf. on Boundary Element Methods, Southampton, September, 1988; Southampton: Computational Mechanics Pubs.
Bush, M. B.; Phan-Thien, N. (1985): Drag force on a sphere in creeping motion through a Carreau model fluid. J. Non-Newtonian Fluid Mech. 16, 303–313
Bush, M. B.; Tanner, R. I. (1983): Numerical solution of viscous flows using integral equation methods. Int. J. Num. Meth. Fluids 3, 71–92
Coleman, C. J. (1990): A boundary element approach to some non-linear equations from fluid mechanics. Comp. Mech. 6, 197–202
Dheur, J.; Crochet, M. J. (1987): Newtonian stratified flow through an abrupt expansion. Rheol. Acta 26, 401–413
Dheur, J.; Crochet, M. J. (1989): Stratified flows of Newtonian and viscoelastic fluids. J. Non-Newtonian Fluid Mech. 32, 1–18
Doblare, M. (1987): Computational aspects of the boundary element method. In: Brebbia, C. A. (ed): Topics of boundary element research, vol. 3 Berlin, Heidelberg, New York: Springer
Hsiao, G. C. (1988): The coupling of BEM and FEM—A brief review. In: Brebbia, C. A. (ed): Boundary elements X, vols. 1, pp. 431–445. Southampton: Computational Mechanics Pubs.
Karagiannis, A.; Mavridis, H.; Hrymak, A. N., Vlachopoulos, J. (1988): Interface determination in bicomponent extrusion. Polym. Eng. Sci. 28, 982
Kelmanson, M. A. (1983): Boundary integral equation solution of viscous flows with a free surface. J. Eng. Math. 17, 329–343
Ladyzhenskaya, O. A. (1963): The mathematical theory of viscous incompressible flow. U.S.A., Gordon and Breach
Liggett, J. A.; Liu, P. L.-F. (1983): The boundary integral equation method for porous media flow. London: Allen and Unwin
Mackerle, J.; Brebbia, C. A. (1988): The boundary element reference book. Southampton: Computational Mechanics Pubs.
Mavridis, H.; Hrymak, A. N.; Vlachopoulos, J. (1987): Finite element simulation of stratified multiphase flows. AIChEJ. 33, 410
Mitsoulis, E. (1986): Extrudate swell in double-layer flows. J. Rheology 30, S23-S44
Mitsoulis, E.; Heng, F. L. (1987): Numerical simulation of coextrusion from a circular die. J. Appl. Polym. Sci. 34, 1713
Musarra, S.; Keunings, R. (1989): J. Non-Newtonian Fluid Mech. 32, 253
Phuoc, H. B.; Tanner, R. I. (1980): Thermally-induced extrudate swell. J. Fluid Mech. 98, 253–271
Tang, W. (1988): Transforming Domain into Boundary Integrals in BEM. Lecture notes in engineering 35. Berlin, Heidelberg, New York: Springer
Tanner, R. I. (1980): A new inelastic theory of extrudate swell. J. Non-Newtonian Fluid Mech. 6, 289–302
Telles, J. C. F.; Brebbia, C. A. (1981): Boundary element solution for half plane problems. Int. J. Solids Struct. 17, 1149–1158
Tosaka, N. (1989): Integral equation formulations with primitive variables for incompressible viscous fluid flow problems. Comp. Mech. 4, 89–103
Tran-Cong, T.; Phan-Thien, N. (1986): Boundary element solution for half space Stokes problems with a no-slip boundary. Comp. Mech. 1, 259–268
Wendland, W. L. (1985): Asymptotic accuracy and convergence for point collocation methods. In: Brebbia, C. A (ed): Topics of boundary element research, vol. 2, pp. 230–258. Berlin, Heidelberg, New York: Springer
Wu, J. C. (1982): Problems of general viscous flow. In: Banerjee, P. K.; Shaw, R. P. (eds): Developments in boundary element methods, vol. 2. London: Appl. Sci.
Youngren, G. K.; Acrivos, A. (1975): Stokes flow past a particle of arbitrary shape: a numerical method of solution. J. Fluid Mech. 69, 377–403
Author information
Authors and Affiliations
Additional information
Communicated by R. I. Tanner, April 16, 1990
Rights and permissions
About this article
Cite this article
Bush, M.B. Stratified newtonian flow calculations by the boundary element method. Computational Mechanics 7, 195–204 (1991). https://doi.org/10.1007/BF00369979
Issue Date:
DOI: https://doi.org/10.1007/BF00369979