Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.707591
Title: Adaptive mesh methods for numerical weather prediction
Author: Cook, Stephen
Awarding Body: University of Bath
Current Institution: University of Bath
Date of Award: 2016
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Abstract:
This thesis considers one-dimensional moving mesh (MM) methods coupled with semi-Lagrangian (SL) discretisations of partial differential equations (PDEs) for meteorological applications. We analyse a semi-Lagrangian numerical solution to the viscous Burgers’ equation when using linear interpolation. This gives expressions for the phase and shape errors of travelling wave solutions which decay slowly with increasing spatial and temporal resolution. These results are verified numerically and demonstrate qualitative agreement for high order interpolants. The semi-Lagrangian discretisation is coupled with a 1D moving mesh, resulting in a moving mesh semi-Lagrangian (MMSL) method. This is compared against two moving mesh Eulerian methods, a two-step remeshing approach, solved with the theta-method, and a coupled moving mesh PDE approach, which is solved using the MATLAB solver ODE45. At each time step of the SL method, the mesh is updated using a curvature based monitor function in order to reduce the interpolation error, and hence numerical viscosity. This MMSL method exhibits good stability properties, and captures the shape and speed of the travelling wave well. A meteorologically based 1D vertical column model is described with its SL solution procedure. Some potential benefits of adaptivity are demonstrated, with static meshes adapted to initial conditions. A moisture species is introduced into the model, although the effects are limited.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.707591  DOI: Not available
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