Publications
97 results found
Kramer SC, Cotter CJ, Pain CC, 2010, Solving the Poisson equation on small aspect ratio domains using unstructured meshes, OCEAN MODELLING, Vol: 35, Pages: 253-263, ISSN: 1463-5003
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- Citations: 13
Ham DA, Farrell PE, Gorman GJ, et al., 2009, Spud 1.0: generalising and automating the user interfaces of scientific computer models, GEOSCIENTIFIC MODEL DEVELOPMENT, Vol: 2, Pages: 33-42, ISSN: 1991-959X
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- Citations: 10
Kramer SC, Stelling GS, 2008, A conservative unstructured scheme for rapidly varied flows, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Vol: 58, Pages: 183-212, ISSN: 0271-2091
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- Citations: 42
Ham DA, Kramer SC, Stelling GS, et al., 2007, The symmetry and stability of unstructured mesh C-grid shallow water models under the influence of Coriolis, Ocean Modelling, Vol: 16, Pages: 47-60, ISSN: 1463-5003
The symmetry and stability properties of two unstructured C-grid discretisations of the shallow water equations are discussed. We establish that a scheme in which the circumcentres of the mesh triangles are used as the surface elevation points has advantageous symmetry properties and derive a Coriolis discretisation which preserves these properties. It is shown that the resulting scheme is conservative in a discretised energy norm. We then establish that schemes in which the water surface elevations are stored at the mesh triangle centroids do not share these advantageous symmetry properties. Finally we show examples which demonstrate that the centroid based scheme is subject to unstable growing modes, particularly in long timescale, Coriolis dominated problems; while the energy conservative circurricentre based scheme suffers from no such limitation. We conclude that unstructured C-grid methods using the triangle circumcentres and the conservative Coriolis scheme derived here therefore have advantages for this sort of problem over those schemes based on centroids. (c) 2006 Elsevier Ltd. All rights reserved.
Kramer SC, Stelling GS, 2006, Parallelisation of inundation simulations, Parallel Computational Fluid Dynamics 2005, Pages: 357-364, ISBN: 9780444522061
The chapter presents parallelization of an inundation model. The chapter focuses on parallelization of the matrix solver that combines a direct Gaussian elimination method with the iterative conjugate gradient algorithm. It is similar to the reduced system conjugate gradient method, and it is applicable not only to the problems that allow a red-black ordering of the equations but to a more general class of unstructured sparse matrices. These arise in the discretization of the flow equations on the combined 1D-2D grid of channel networks and flooded land that are used in the inundation model. With a simple parallelization strategy, the elimination process remains strictly local, and good scaling behavior is achieved. The most important part of parallelization is that of the applied matrix solver. © 2006 Elsevier B.V. All rights reserved.
Kramer SC, Kree R, 2002, Pattern formation of ion channels with state-dependent charges and diffusion constants in fluid membranes, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol: 65, ISSN: 1539-3755
A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electrodiffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode, or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive nonlinear evolution equations near the transitions to stationary patterns. © 2002 The American Physical Society.
Zatz HR, 1993, Galerkin radiosity, SIGGRAPH93: 20th Annual Conference and Exhibition on Computer Graphics and Interactive Techniques, Publisher: ACM
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