18 research outputs found

    A mathematica‐based CAL matrix‐theory tutor for scientists and engineers

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    Under the TLTP initiative, the Mathematics Departments at Imperial College and Leeds University are jointly developing a CAL method directed at supplementing the level of mathematics of students entering science and engineering courses from diverse A‐level (or equivalent) backgrounds. The aim of the joint project is to maintain — even increase ‐ the number of students enrolling on such first‐year courses without lowering the courses’ existing mathematical standards

    Adaptive finite element simulation of three-dimensional surface tension dominated free-surface flow problems

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    An arbitrary Lagrangian--Eulerian finite element method is described for the solution of time-dependent, three-dimensional, free-surface flow problems. Many flows of practical significance involve contact lines, where the free surface meets a solid boundary. This contact line may be pinned to a particular part of the solid but is more typically free to slide in a manner that is characterised by the dynamic contact angle formed by the fluid. We focus on the latter case and use a model that admits spatial variation of the contact angle: thus permitting variable wetting properties to be simulated. The problems are driven by the motion of the fluid free surface (under the action of surface tension and external forces such as gravity) hence the geometry evolves as part of the solution, and mesh adaptivity is required to maintain the quality of the computational mesh for the physical domain. Continuous mesh adaptivity, in the form of a pseudo-elastic mesh movement scheme, is used to move the interior mesh nodes in response to the motion of the fluid's free surface. Periodic, discrete remeshing stages are also used for cases in which the fluid volume has grown, or is sufficiently distorted, by the free-surface motion. Examples are given of a droplet sliding on an inclined uniform plane and of a droplet spreading on a surface with variable wetting properties

    Integral equation analysis of the driven-cavity boundary singularity

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    AbstractA specially-modified boundary integral equation (BIE) method is used to investigate the viability of the singular boundary conditions of the well known driven-cavity Stokes flow problem, a bench-mark problem of computational fluid dynamics. We introduce small ‘leaks’ to replace the singularities, thus creating a perturbed, physically realizable problem. We make two discoveries, namely: (i) unexpectedly, the introduction of the leaks affects the flow field at considerably greater distances from the leaks than one might perhaps intuitively predict; and (ii) the full, numerical BIE solution reveals that the far field, asymptotic, closed-form solution for the flowfield of the perturbed problem is a surprisingly accurate representation of the flow even in the near field

    On the stability of viscous free-surface flow supported by a rotating cylinder

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    Using an adaptive finite-element (FE) scheme developed recently by the authors, we shed new light on the long-standing fundamental problem of the unsteady free-surface Stokes flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field. For supportable loads, we observe that the steady-state is more readily attained for near-maximal fluid loads on the cylinder than for significantly sub-maximal loads. For the latter, we investigate large-time dynamics by means of a finite-difference approximation to the thin-film equations, which is also used to validate the adaptive FE simulations (applied to the full Stokes equations) for these significantly sub-maximal loads. Conversely, by comparing results of the two methods, we assess the validity of the thin-film approximation as either the load is increased or the rotation rate of the cylinder is decreased. Results are presented on the independent effects of gravity, surface tension and initial film thickness on the decay to steady-state. Finally, new numerical simulations of load shedding are presented

    Finite element simulation of three-dimensional free-surface flow problems

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    An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

    A zonal boundary element method for analysing heat exchangers with thin extended surfaces

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    AbstractWe present a zonal boundary element method (ZBEM) for the rapid, efficient, and accurate solution of the temperature distribution within extended surfaces whose aspect ratio may be asymptotically large. Our ZBEM employs a block-tridiagonal-matrix solution technique which decouples information which is ‘far apart’ with respect to the smallest dimension of the (asymptotically-thin) solution domain. We calculate asymptotic results for the performance advantage of the ZBEM over the classical BEM (CBEM), which are shown to be in excellent agreement with those of our numerical implementation. We propose that the ZBEM permits solution of asymptotically-large problems on modest computational platforms
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