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Numerical modelling of geophysical fluids on geodesic grids

Grant number: 14/10750-0
Support type:Scholarships abroad - Research
Effective date (Start): February 04, 2015
Effective date (End): February 03, 2016
Field of knowledge:Physical Sciences and Mathematics - Geosciences - Meteorology
Principal researcher:Pedro da Silva Peixoto
Grantee:Pedro da Silva Peixoto
Host: John Thuburn
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: University of Exeter, Exeter, England  


Global numerical models for weather and climate simulations historically employ latitude-longitude grids on the sphere. However, the pole singularities and the related anisotropies tend to cause a loss of computational efficiency in modern massively parallel computers. Several research groups have been investigating alternatives, considering more isotropic spherical grids. One of the most promising approaches seems to be the geodesic grids, formed by polygonal geodesic cells.An important step in the development of weather or climate models is the study of simplified models, including shallow water models, which describe most of the horizontal dynamical processes of the atmosphere. Although many shallow water models on icosahedral grids have already been developed, there are still open questions related to the discretizations and many issues to be addressed. An efficient approach is to use finite volume methods with good mimetic properties, such as the ones proposed in \cite{Thuburn2009} and \cite{Ringler2010}. This methodology is very low accurate, essentially due its strong geometry dependency, which is irregular in geodesic grids. Nevertheless, it is currently being used with success, for example, on the MPAS model \cite{Skamarock2012}. Based on previous works (\cite{Peixoto2013, Peixoto2014}), where we analysed some relations between cell geometries and finite volume discretizations, we believe that the approach of \cite{Thuburn2009} may be improved.Also, the use of semi-Lagrangian semi-implicit schemes, for example, has still been little explored within geodesic grids. This methodology has been applied in grid-point and spectral models with great success. From our previous work (\cite{Peixoto2013b}), in which we developed a semi-Lagrangian transport model on geodesic icosahedral grids, we believe that this approach will be successful for other models as well.We intend to work on these two front-lines for one year together with Prof. John Thuburn and the GungHo project group, who are currently developing the Highly Optimized Globally Uniform Next Generation Model in UK. The project will be developed within the University of Exeter's dependencies with collaborations with the Met Office and other universities involved with the GungHo project. (AU)

News published in Agência FAPESP Newsletter about the scholarship:
Nova geração da Matemática brasileira se reúne em congresso em São Paulo 
New generation of Brazilian mathematicians gathers at São Paulo conference 
Una nueva generación de matemáticos brasileños se reúne en un congreso en São Paulo 

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
SCHREIBER, MARTIN; PEIXOTO, PEDRO S.; HAUT, TERRY; WINGATE, BETH. Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems. INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS, v. 32, n. 6, SI, p. 913-933, NOV 2018. Web of Science Citations: 3.
BELL, MICHAEL J.; PEIXOTO, PEDRO S.; THUBURN, JOHN. Numerical instabilities of vector-invariant momentum equations on rectangular C-grids. QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, v. 143, n. 702, A, UNDEFINED, UNDEFINED, p. 563-581, JAN 2017. Web of Science Citations: 12.
PEIXOTO, PEDRO S. Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative. Journal of Computational Physics, v. 310, p. 127-160, APR 1 2016. Web of Science Citations: 11.

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