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Projects: Projects for Investigator
Reference Number EP/W007436/1
Title Efficient numerical methods for wave-action transport and scattering
Status Completed
Energy Categories Not Energy Related 90%;
Other Cross-Cutting Technologies or Research(Other Supporting Data) 10%;
Research Types Basic and strategic applied research 100%
Science and Technology Fields PHYSICAL SCIENCES AND MATHEMATICS (Applied Mathematics) 100%
UKERC Cross Cutting Characterisation Not Cross-cutting 100%
Principal Investigator Dr J Vanneste
No email address given
Sch of Mathematics
University of Edinburgh
Award Type Standard
Funding Source EPSRC
Start Date 01 January 2022
End Date 31 December 2022
Duration 12 months
Total Grant Value £61,854
Industrial Sectors No relevance to Underpinning Sectors
Region Scotland
Programme NC : Maths
Investigators Principal Investigator Dr J Vanneste , Sch of Mathematics, University of Edinburgh (100.000%)
  Industrial Collaborator Project Contact , New York University, USA (0.000%)
Project Contact , Goethe University of Frankfurt am Main (0.000%)
Web Site
Abstract Waves propagating in the atmosphere and ocean need to be represented in the numerical models used for weather and climate prediction in order to capture the strong impact they have on the atmospheric and oceanic circulation, on the state of the sea surface, and on the transport of pollutants. This cannot be achieved directly, however, because the typical wavelengths are much shorter than the grid scales of even the highest resolution numerical models. A reduced mathematical model that averages over the short wavelengths offers a solution but poses a major computational challenge. It describes the distribution of wave-action density in an extended position-wavenumber phase space; hence, it requires solving a partial differential equation in up to 6 space-like dimensions. This is beyond the reach of traditional discretisation methods. This project aims at demonstrating the feasibility of an alternative approach, based on a dynamical low-rank approximation of the wave-action density. This approach expands the wave action as a sum of products of functions of a few variables, constructed on-the-fly to project the dynamics onto the space of low-rank functions while minimising an error. The project will formulate an algorithm based on low-rank approximation and splitting, implement two versions that use different combinations of grid-based and spectral discretisations, and test them against a ray-tracing algorithm (specifically designed to capture the dynamics of a few wavepackets) and against direct numerical simulations of the underlying fluid equations. The formulation and implementation will emphasise parallelisation and efficiency on supercomputers, with testing carried out on ARCHER2. The project primarily targets the modelling of internal waves, with a focus on the representation of their scattering by turbulence and of nonlinear wave-wave interactions. Applications to ocean surface waves will also be considered
Publications (none)
Final Report (none)
Added to Database 02/02/22