Sefydliad Gwyddorau Cyfrifiadurol a Mathemategol Cymru SGCMC

1. SefydliadGwyddorauCyfrifiadurol a Mathemategol Cymru SGCMC WIMCS Wales Institute of Mathematical and Computational Sciences Computational Modelling Research interests include: Hp-FEM for eddy current analysis Modelling of droplet splashing Motivation Eddy current analysis is important for many industrial applications of electromagnetism, including inductive heating, non-destructive testing and electromagnetic braking. For many electromagnetic machines, eddy currents represent unwanted effects that should be minimized. Aim Conductors in industrial applications are often multiply connected. The aim of this joint work with Dr Zaglmayr, Graz University of Technology, is to obtain accurate finite element solutions of Maxwell’s equations on these geometries. Method The eddy current model is described by Common approaches involve the introduction of scalar or vector potentials to simplify the computational complexity of the problem. However, the De-Rham sequence is only exact when the domain is contractable Cohomology spaces must then be added to regain exactness. The dimension of these spaces depends on the topology of the domain. Using hp basis functions, designed for the complete sequence, an efficient preconditioner has been developed for the resulting complex symmetric linear system. Outcome Publications P.D. Ledger, S. Zaglmayr, hp-Finite element simulation of three dimensional eddy current problems on multiply connected domains. Computer Methods in Applied Mechanics and Engineering,doi:10.1016/j.cma.2010.07.010 Next Steps Using hp FEM in the solution of inverse problems with M. Marletta, B.M. Brown Motivation Droplet impact and splashing on solid surfaces is a key element for many industrial processes: direct fuel injection in internal engines, gas turbines, spray cooling of steel sheets, spray coating and spray painting. It is, therefore, important to study the fundamentals of droplet impact and splashing. Aim We aim to develop a highly reliable numerical framework, which can handle a wide range of free surface flow phenomena, and numerically study the fundamentals of droplet impact and splashing. Method The methodology is based on a Cartesian grid system and consists of the level set method, the VOF (Volume of Fluid) method, the CIP-CSL method, VSIAM3 and the CSF model. The numerical framework was developed when the author was in the research group of Prof Osher at UCLA. Outcome The numerical methodology can capture the physics of droplet splashing, as shown in the figures. The grid size is 200x200x100. All parameters are quantitative. We found that the dynamic contact angle plays an important role in the formation of the droplet splash. Publications Kensuke Yokoi, Damien Vadillo, John Hinch and Ian Hutchings, Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface, Physics of Fluids, 21, 072102 (2009). Kensuke Yokoi, A numerical method for free-surface flows and its application to droplet impact on a thin liquid layer, Journal of Scientific Computing, 35, 372 (2008). Next Steps We will study various attractive free surface flow problems, including industrial as well as scientific applications, such as atomisation. Showcase Workshops Higher Order Methods in Computational Science and EngineeringOne day workshop organised by Dr P.D. Ledger on 15th May 2008. Invited talks by Professors Ainsworth (Strathclyde University) , Houston (The University of Nottingham), Phillips (Cardiff University) and Sherwin (Imperial College). Attended by over 40 participants from WIMICS and beyond. The topics that were presented included computable error bounds for mixed, TETRAHEDRON III Two day workshop organised by Professors O. Hassan and K. Morgan, 14th–15th September 2010. Tetrahedron I was held in Berlin in 2005 and Tetrahedron II in Paris in 2007. The main topics of interest were the latest developments in unstructured mesh generation methods for volumes and surfaces, adaptive and anisotropic mesh generation, meshing for biomedical applications and automatic geometrical feature identification, allowing for automatic geometrical reduction and repair. Many of the internationally leading groups in mesh generation were represented. The next Workshop in the series will be held in Milan. non-conforming and discontinuous Galerkin finite elements, adaptive hp-discontinous Galerkin for incompressible flow, the prediction of complex flows using spectral elements and direct optimal growth for timesteppers. Future Cluster Activites The major event for the Cluster in 2011 will be the Follow–Up Meeting on Computational Challenges in Partial Differential Equations, organised jointly with the Isaac Newton Institute. The Meeting will be held at Swansea University, 4th–8th April, 2011. Building on the success of a six month programme in this area at the Isaac Newton Institute in 2003, the Meeting will concentrate upon a number of areas that are currently attracting significant interest within the community. Thirty two international experts will contribute to eight half--day sessions in multiscale modelling, partial differential equations on surfaces and geometric evolution problems, interface modelling, computational rheology, atomistic--to--continuum passage, density functional theory and quasi--continuum methods, low--order modelling: widening the range of high--fidelity time--dependent simulations, uncertainty modelling and biomedical applications, including new modelling techniques and patient--specific techniques. Poster Presenters: Dr P Ledger, Dr K Yokoi