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SIAM Chapter Meetings 2012-2013

Programme

These meetings take place in Room M/2.06, Senghennydd Road, Cardiff, from 4pm, unless otherwise stated. Everyone is welcome to attend. If you wish to give a talk, please email siam@cardiff.ac.uk.

16th October 2012

Speaker: Yousef Ghaffari Motlagh (School of Engineering)

Title: Isogeometric Analysis of Laminar and Turbulent Flows

Abstract: The residual-based Variational Multiscale Method is applied to three dimensional flows within concentric and eccentric annuli, and about circular cylinders, in laminar and turbulent flow regimes. Isogeometric discretizations using NURBS basis functions enable exact modelling of all geometries. When applied to laminar flows, optimal rates of convergence to exact analytical solutions are observed. Medium mesh resolution of turbulent flows produce good LES quality solutions, and fine mesh resolution of turbulent flows converge to benchmark DNS solutions. The isogeometric modelling approach also enable modelling and solution of flows about touching cylinders, in which a singularity is created. A unique feature of the approach is that precisely the same method and computer code is used for all these simulations with no changes whatsoever for each case. This establishes the potential of the isogeometric residual-based Variational Multiscale method for calculating practical engineering flows which often involve both laminar and turbulent subregimes.

27th November 2012

Speaker: Alan Walker (University of Glamorgan)

Title: The use of Fractal Geometry in the Design of Piezoelectric Ultrasonic Transducers

Abstract: Ultrasound is used in a variety of applications in non-destructive evaluation, medical imaging, defense and dentistry. Piezoelectric ultrasonic transducers convert electrical energy to mechanical, and vice versa. The geometry of composite piezoelectric ultrasonic transducers is typically regular and periodic with one dominant length scale. In many applications there is motivation to design transducers that operate over a wide bandwidth so that, for example, signals containing a broad frequency content can be received. The device's length scale will dictate the central operating frequency of the device and so, in order to construct a wide bandwidth device, it would seem natural to design a device that contains a range of length scales. This presentation will consider one such transducer design. For the composite geometry a fractal medium is chosen as this contains a wide range of length scales. A theoretical model is developed and numerical results will be presented. They suggest that this device would have a three-fold improvement in the reception sensitivity bandwidth as compared to a conventional composite design. Finite-element analysis will provide information on the effect of poling on the device's performance. A preliminary experimental investigation has been undertaken, with a Sierpinski gasket fractal transducer design, and the good correlation between simulated and experimentally measured operation will be presented.

19th February 2013

Speaker: Michael Strauss (School of Mathematics)

Title: Eigenvalue Approximation for Schrodinger and Dirac Operators.

Abstract: I will discuss methods for approximating eigenvalues of self-adjoint operators. In particular, a new perturbation technique which appears to work extremely well. I will apply the results to Schrodinger, Dirac and Magnetohydrodynamics operators.

16th April 2013

Speaker: Claire Heaney (School of Engineering)

Title: Adaptive Mesh Refinement: Its Application to Geotechnical Problems.

Abstract: Adaptive Mesh Refinement (AMR) techniques have been developed extensively over the last two decades and have been successfully applied in various fields including astrophysics, fluid dynamics, radiation transfer. The aim of the method is to detect where the discretisation error is largest, and then to refine the mesh in this part of the domain. For applications where physical behaviour develops on several well-separated scales, use of this technique saves computational effort by having a fine mesh only where it is required.

This seminar will (i) introduce the different techniques involved in AMR, including recovery, error estimation, mesh refinement and data transfer (ii) outline the implementation of AMR within PLAXIS, a finite element solver designed to tackle geotechnical problems (iii) show some results for the biaxial compression test and the failure of a slope.