Two-zone model of shear dispersion in a channel using centre manifolds
Article
Roberts, A. J. and Strunin, Dmitry V.. 2004. "Two-zone model of shear dispersion in a channel using centre manifolds." The Quarterly Journal of Mechanics and Applied Mathematics. 57 (3), pp. 363-378. https://doi.org/10.1093/qjmam/57.3.363
| Article Title | Two-zone model of shear dispersion in a channel using centre manifolds |
|---|---|
| ERA Journal ID | 368 |
| Article Category | Article |
| Authors | Roberts, A. J. (Author) and Strunin, Dmitry V. (Author) |
| Journal Title | The Quarterly Journal of Mechanics and Applied Mathematics |
| Quarterly Journal of Mechanics and Applied Mathematics | |
| Journal Citation | 57 (3), pp. 363-378 |
| Number of Pages | 22 |
| Year | 2004 |
| Place of Publication | Oxford, England |
| ISSN | 0033-5614 |
| 1464-3855 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1093/qjmam/57.3.363 |
| Abstract | [Summary]: To achieve better precision in describing contaminant dispersion in channels some authors resort to dividing a channel into two zones, fast and slow, leading to a pair of coupled evolution equations for cross-sectionally-averaged concentrations in the zones. We construct a two-zone model whose accuracy is guaranteed by centre manifold theory. The model leads to evolution equations that differ from existing models. We also formulate modified initial conditions for the model to obtain closer correlation between the manifold solution and real solution. Effectiveness of the modified initial conditions is demonstrated numerically by a comparison between the manifold solution and direct numerical simulations of the original advection–diffusion equations. |
| Keywords | two-zone model; shear dispersion; channels; centre manifolds |
| ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |
| 401706. Numerical modelling and mechanical characterisation | |
| Public Notes | Deposited in accordance with the copyright policy of the publisher. This is an electronic version of an article published in Quarterly Journal of Mechanics and Applied Mathematics, 57 (3), 363-378. |
| Byline Affiliations | Department of Mathematics and Computing |
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Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2001. "Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena." Mechanics Research Communications. 28 (6), pp. 637-651. https://doi.org/10.1016/S0093-6413(02)00216-1A holistic finite difference approach models linear dynamics consistently
Roberts, A. J.. 2003. "A holistic finite difference approach models linear dynamics consistently." Mathematics of Computation. 72 (241), pp. 247-262. https://doi.org/10.1090/S0025-5718-02-01448-5Holistic discretisation ensures fidelity to Burger's equation
Roberts, A. J.. 2001. "Holistic discretisation ensures fidelity to Burger's equation." Applied Numerical Mathematics. 37 (3), pp. 371-396. https://doi.org/10.1016/S0168-9274(00)00053-2A lubrication model of coating flows over a curved substrate in space
Roy, R. Valery, Roberts, A. J. and Simpson, M. E.. 2002. "A lubrication model of coating flows over a curved substrate in space." Journal of Fluid Mechanics. 454 (1), pp. 235-261. https://doi.org/10.1017/S0022112001007133Nonlinear instability in generalized nonlinear phase diffusion equation
Strunin, Dmitry V.. 2003. "Nonlinear instability in generalized nonlinear phase diffusion equation." Progress of Theoretical Physics Supplement.Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids
Roberts, A. J.. 2007. Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids . University of Southern Queensland.Computer algebra derives normal forms of stochastic differential equations
Roberts, A. J.. 2007. Computer algebra derives normal forms of stochastic differential equations . Toowoomba, Australia. University of Southern Queensland.Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation
Roberts, A. J.. 2006. Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation. Toowoomba, Australia. University of Southern Queensland.The style files: favour the present tense
Roberts, Tony. 2006. "The style files: favour the present tense." Gazette of the Australian Mathematical Society. 33 (5), pp. 313-314.The style files: explicitly avoid false conditionals
Roberts, Tony. 2006. "The style files: explicitly avoid false conditionals." Gazette of the Australian Mathematical Society. 33 (4), pp. 241-242.The style files: inform with titles, abstracts and introductions
Roberts, Tony. 2006. "The style files: inform with titles, abstracts and introductions." Gazette of the Australian Mathematical Society. 33 (3), pp. 169-170.The style files: clarify this
Roberts, Tony. 2006. "The style files: clarify this." Gazette of the Australian Mathematical Society. 33 (2), pp. 104-105.The style files: prefer active writing to passive
Roberts, Tony. 2006. "The style files: prefer active writing to passive." Gazette of the Australian Mathematical Society. 33 (1), pp. 22-23.Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, A. J.. 2005. Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations. Toowoomba, Australia. University of Southern Queensland.