Numerical solution of the freesurface viscous flow on a horizontal rotating elliptical cylinder
Hunt, R. (2007) Numerical solution of the freesurface viscous flow on a horizontal rotating elliptical cylinder. Numerical Methods for Partial Differential Equations, 24 (4). pp. 10941114. ISSN 0749159X (http://dx.doi.org/10.1002/num.20307)
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The numerical solution of the freesurface fluid flow on a rotating elliptical cylinder is presented. Up to the present, research has concentrated on the circular cylinder for which steady solutions are the main interest. However, for noncircular cylinders, such as the ellipse, steady solutions are no longer possible, but there will be periodic solutions in which the solution is repeated after one full revolution of the cylinder. It is this new aspect that makes the investigation of noncircular cylinders novel. Here we consider both the timedependent and periodic solutions for zero Reynolds number fluid flow. The numerical solution is expedited by first mapping the fluid film domain onto a rectangle such that the position of the freesurface is determined as part of the solution. For the timedependent case a simple timemarching method of lines approach is adopted. For the periodic solution the discretised nonlinear equations have to be solved simultaneously over a time period. The resulting large system of equations is solved using Newton's method in which the form of the Jacobian enables a straightforward decomposition to be implemented, which makes matrix inversion manageable. In the periodic case all derivatives have been approximated pseudospectrally with the time derivative approximated by a differentiation matrix which has been specially derived so that the weight of fluid is algebraically conserved. Of interest is the solution for which the weight of fluid is at its maximum possible value, and this has been obtained by increasing the weight until a consistency breakdown occurs. Timedependent solutions do not produce the periodic solution after a long timescale but have protuberances which are constantly appearing and disappearing. Periodic solutions exhibit spectral accuracy solutions and maximum supportable weight solutions have been obtained for ranges of eccentricity and angular velocity. The maximum weights are less than and approximately proportional to those obtained for the circular case. The shapes of maximum weight solutions is distinctly different from submaximum weight solutions.


Item type: Article ID code: 5433 Dates: DateEventNovember 2007PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics > Mathematics Depositing user: Strathprints Administrator Date deposited: 26 Feb 2008 Last modified: 08 Apr 2024 16:16 URI: https://strathprints.strath.ac.uk/id/eprint/5433