Publications
71 results found
Cotter CJ, Ham DA, Pain CC, 2009, A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling, Ocean Modelling, Vol: 26, Pages: 86-90, ISSN: 1463-5003
We introduce a mixed discontinuous/continuous finite element pair for ocean modelling, with continuous quadratic layer thickness and discontinuous velocity. We investigate the finite element pair applied to the linear shallow-water equations on an f-plane. The element pair has the property that all geostrophically balanced states which strongly satisfy the boundary conditions have discrete divergence equal to exactly zero and hence are exactly steady states of the discretised equations. This means that the finite element pair has excellent geostrophic balance properties. We also show that the element pair applied to the non-rotating linear shallow-water equations does not have any spurious small eigenvalues. We illustrate these properties using numerical tests and provide convergence calculations which show that the numerical solutions have errors which decay quadratically with element edge length for both velocity and layer thickness.
Cotter CJ, Ham DA, Pain CC, et al., 2009, LBB stability of a mixed Galerkin finite element pair for fluid flow simulations, Journal of Computational Physics, Vol: 228, Pages: 336-348
We introduce a new mixed finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1D–P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the LBB stability condition and hence has no spurious zero-energy modes. The advantage of this particular element choice is that the mass matrix for velocity is block diagonal so it can be trivially inverted; it also allows the order of the pressure to be increased to quadratic whilst maintaining LBB stability which has benefits in geophysical applications with Coriolis forces. We give a normal mode analysis of the semi-discrete wave equation in one dimension which shows that the element pair is stable, and demonstrate that the element is stable with numerical integrations of the wave equation in two dimensions, an analysis of the resultant discrete Laplace operator in two and three dimensions on various meshes which shows that the element pair does not have any spurious modes. We provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic.
Ham DA, Pain CC, Hanert E, et al., 2009, Special Issue: The sixth international workshop on unstructured mesh numerical modelling of coastal, shelf and ocean flows. Imperial College London, September 19-21, 2007, Ocean Modelling, Vol: 28, ISSN: 1463-5003
Ham D, Farrell P, Gorman G, et al., 2008, Spud
Spud is a generic system for defining, writing and processing options files for scientific computer models.The interfaces to scientific computer models are frequently primitive, under-documented and ad-hoc text files. This makes using and developing the model in question difficult and error-prone.With Spud, the model developer need only write a rules file (schema) which defines the options which the model takes and the relationship between them. The Spud component Diamond then provides an automatically generated graphical user interface which guides the user and validates the user's input against the schema. Diamond writes out an xml options file for use in Spud.The developer then uses libspud to read the options file into the model. Libspud can read any valid options file without further code modifications and makes the options available at any point in the model code at which they are required.Spud further provides the facility for the schema to be self-documenting and Diamond presents this documentation to the model user in a context-sensitive manner.
Pietrzak J, Socquet A, Ham D, et al., 2007, Defining the source region of the Indian Ocean Tsunami from GPS, altimeters, tide gauges and tsunami models, EARTH PLANET SC LETT, Vol: 261, Pages: 49-64, ISSN: 0012-821X
To understand the role of the co-seismic moment magnitude, M-w, 9.1-9.3 Sumatra-Andaman Earthquake rupture mechanism on the severity of the Indian Ocean Tsunami, we used permanent Global Positioning System (GPS) data and carried out an analysis of co-seismic displacement and tsunami models. Tsunami modelling, validated against independent Jason-I altimetry data and tsunami arrival time data as determined from tide gauges, was used to analyse the results of five co-seismic slip inversions, using GPS, seismicity and/or uplift data. In this way we determined the most likely slip distribution characterized by slip maxima of similar to 20 m in the South and similar to 20 m in the North. We used both the distribution and temporal evolution of the co-seismic slip as derived from the GPS data. We show that the similar to 9 min propagation time of the rupture led to constructive interference of waves radiating first from the South and minutes later from the North, strengthening the tsunami in Southern India, Sri Lanka and Thailand. We conclude that the incorporation of permanent real-time GPS stations would represent a valuable component of future tsunami warning systems. (C) 2007 Elsevier B.V All rights reserved.
Piggott MD, Pain CC, Gorman GJ, et al., 2007, Multi-scale ocean modelling with adapting unstructured grids, CLIVAR Exchanges, Vol: 12, Pages: 21-23, ISSN: 1026-0471
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.
Ham DA, Pietrzak J, Stelling GS, 2006, A streamline tracking algorithm for semi-Lagrangian advection schemes based on the analytic integration of the velocity field, JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, Vol: 192, Pages: 168-174, ISSN: 0377-0427
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Ham DA, Pietrzak J, Stelling GS, 2006, A streamline tracking algorithm for semi-Lagrangian advection schemes based on the analytic integration of the velocity field, Journal of Computational and Applied Mathematics, Vol: 192, Pages: 168-174
A new scheme for the construction on an unstructured grid of the streamlines of the three-dimensional shallow water equations is presented. The qualitative advantages of the scheme, notably closed streamlines and realistic treatment of closed boundaries, are derived and the spatial accuracy is demonstrated. Semi-Lagrangian advection schemes offer the computational cost advantage of being explicit but also unconditionally stable with respect to time step. However, semi-Lagrangian methods based on the numerical integration of the discretised velocity field frequently have difficulty in meeting physically significant criteria such as the closure of streamlines and the inviolability of closed boundaries. Here a streamline tracking scheme based on the analytic integration of the discretised velocity field is presented.
Ham DA, Pietrzak J, Stelling GS, 2005, A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations, Ocean Modelling, Vol: 10, Pages: 153-169, ISSN: 1463-5003
We present an unstructured grid finite volume three-dimensional hydrostatic model. An important aspect in 3D models is the choice of horizontal discretisation. For problems that are governed by complex coastal boundaries an unstructured grid approach seems attractive. This paper focuses on the development of a new unstructured grid three-dimensional hydrostatic model. An efficient and highly scalable implicit solution technique is adopted for the solution of the free surface elevation and an semi-Lagrangian approach is adopted for the advection of momentum and scalars. A number of tests are presented which show that the model is capable of simulating Kelvin waves in a circular basin and the North Sea. © 2004 Elsevier Ltd. All rights reserved.
Ham DA, On techniques for modelling coastal and ocean flow with unstructured meshes
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