Compatible finite element methods for atmospheric dynamical cores
File(s)
Author(s)
McRae, Andrew Timothy Tang
Type
Thesis
Abstract
A key part of numerical weather prediction is the simulation of the
partial differential equations governing atmospheric flow over the
Earth's surface. This is typically performed on supercomputers at
national and international centres around the world. In the last decade,
there has been a relative plateau in single-core computing performance.
Running ever-finer forecasting models has necessitated the use of
ever-larger numbers of CPU cores.
Several current forecasting models, including those favoured by the Met
Office, use an underlying latitude--longitude grid. This facilitates the
development of finite difference discretisations with favourable
numerical properties. However, such models are inherently unable to make
efficient use of large numbers of processors, as a result of the
excessive concentration of gridpoints in the vicinity of the poles. A
certain class of mixed finite element methods have recently been
proposed in order to obtain favourable numerical properties on an
arbitrary -- in particular, quasi-uniform -- mesh.
This thesis supports the proposition that such finite element methods,
which we label ``compatible'', or ``mimetic'', are suitable for
discretising the equations used in an atmospheric dynamical core. We
firstly show promising results applying these methods to the nonlinear
rotating shallow-water equations. We then develop sophisticated tensor
product finite elements for use in 3D. Finally, we give a discretisation
for the fully-compressible 3D equations.
partial differential equations governing atmospheric flow over the
Earth's surface. This is typically performed on supercomputers at
national and international centres around the world. In the last decade,
there has been a relative plateau in single-core computing performance.
Running ever-finer forecasting models has necessitated the use of
ever-larger numbers of CPU cores.
Several current forecasting models, including those favoured by the Met
Office, use an underlying latitude--longitude grid. This facilitates the
development of finite difference discretisations with favourable
numerical properties. However, such models are inherently unable to make
efficient use of large numbers of processors, as a result of the
excessive concentration of gridpoints in the vicinity of the poles. A
certain class of mixed finite element methods have recently been
proposed in order to obtain favourable numerical properties on an
arbitrary -- in particular, quasi-uniform -- mesh.
This thesis supports the proposition that such finite element methods,
which we label ``compatible'', or ``mimetic'', are suitable for
discretising the equations used in an atmospheric dynamical core. We
firstly show promising results applying these methods to the nonlinear
rotating shallow-water equations. We then develop sophisticated tensor
product finite elements for use in 3D. Finally, we give a discretisation
for the fully-compressible 3D equations.
Version
Open Access
Date Issued
2015-10
Date Awarded
2016-03
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Cotter, Colin
Ham, David
Sponsor
Imperial College London
European Union
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)