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A Mimetic, Semi-implicit, Forward-in-time, Finite Volume Shallow Water Model: Comparison of Hexagonal–icosahedral and Cubed Sphere Grids : Volume 6, Issue 4 (17/12/2013)

By Thuburn, J.

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Book Id: WPLBN0004009587
Format Type: PDF Article :
File Size: Pages 59
Reproduction Date: 2015

Title: A Mimetic, Semi-implicit, Forward-in-time, Finite Volume Shallow Water Model: Comparison of Hexagonal–icosahedral and Cubed Sphere Grids : Volume 6, Issue 4 (17/12/2013)  
Author: Thuburn, J.
Volume: Vol. 6, Issue 4
Language: English
Subject: Science, Geoscientific, Model
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2013
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Dubos, T., Cotter, C. J., & Thuburn, J. (2013). A Mimetic, Semi-implicit, Forward-in-time, Finite Volume Shallow Water Model: Comparison of Hexagonal–icosahedral and Cubed Sphere Grids : Volume 6, Issue 4 (17/12/2013). Retrieved from http://comicbooklibrary.org/


Description
Description: University of Exeter, College of Engineering, Mathematics and Physical Sciences, Exeter, UK. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids.

Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1.

In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.


Summary
A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed sphere grids

Excerpt
Arakawa, A. and Lamb, V. R.: Computational design of the basic dynamical processes of the UCLA general circulation model, in: General Circulation Models of the Atmosphere, Methods in Computational Physics, vol 17, edited by: Chang, J., Academic Press, San Diego, 172–265, 1977.; Cotter, C. J. and Shipton, J.: Mixed finite elements for numerical weather prediction, J. Comput. Phys., 231, 7076–7091, 2012.; Crowley, W. P.: Numerical advection experiments, Mon. Weather Rev., 96, 1–11, 1968.; Cullen, M. J. P.: On the accuracy of the semi-geostrophic approximation, Q. J. Roy. Meteor. Soc., 126, 1099–1115, 2000.; Du, Q., Faber, V., and Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms, SIAM Rev., 41, 637–676, 1999.; Ford, R., McIntyre, M. E., and Norton, W. A.: Balance and the slow quasimanifold: some explicit results, J. Atmos. Sci., 57, 1236–1254, 2000.; Fulton, S. R., Ciesielski, P. E., and Schubert, W. H.: Multigrid methods for elliptic problems: a review, Mon. Weather Rev., 114, 943–959, 1986.; Galewsky, J., Scott, R. K., and Polvani, L. M.: An initial value problem for testing numerical models of the global shallow-water equations, Tellus A, 56, 429–440, 2004.; Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid, Part I: Basic design and results of tests, Mon. Weather Rev., 123, 1862–1880, 1995a.; Heikes, R. and Randall, D.: Numerical integration of the shallow-water equations on a twisted icosahedral grid, Part II: A detailed description of the grid and analysis of numerical accuracy, Mon. Weather Rev., 123, 1881–1997, 1995b.; Holdaway, D. R. E., Thuburn, J., and Wood, N.: On the relation between order of accuracy, convergence rate and spectral slope for linear numerical methods applied to multiscale problems, Int. J. Numer. Meth. Fl., 56, 1297–1303, 2008.; Kent, J., Thuburn, J., and Wood, N.: Assessing implicit large eddy simulation for two-dimensional flow, Q. J. Roy. Meteor. Soc., 138, 365–376, 2012.; Lashley, R. K.: Automatic generation of accurate advection schemes on unstructured grids and their application to meteorological problems, Ph.D. Thesis, University of Reading, Reading, UK, 2002.; Leonard, B. P.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comp. Methods Appl. Mech. Eng., 19, 59–98, 1979.; Leonard, B. P., MacVean, M. K., and Lock, A. P.: Positivity-preserving numerical schemes for multi-dimensional advection, NASA Technical Memorandum TM-106055 ICOMP-93-05, 1993.; Leonard, B. P., MacVean, M. K., and Lock, A. P.: The flux integral method for multidimensional convection and diffusion, Appl. Math. Model., 19, 333–342, 1995.; Li, S. and Xiao, F.: A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid, J. Comput. Phys., 229, 1774–1796, 2010.; Lin, S.-J. and Rood, R. B.: An explicit flux-form semi-Lagrangian shallow-water model on the sphere, Q. J. Roy. Meteor. Soc., 123, 2477–2498, 1997.; Lipscomb, W. H. and Ringler, T.: An incremental remapping transport scheme on a spherical geodesic grid, Mon. Weather Rev., 133, 2235–2250, 2005.; Miura, H.: An upwind-biased conservative advection scheme for spherical hexagonal–pentagonal grids, Mon. Weather Rev., 135, 4038–4044, 2007.; Rancic, M., Purser, R. J., and Mesinger, F.: A global shallow-water model using an expanded spherical cube: gnomonic versus conformal coordinates, Q. J. Roy. Meteor. Soc., 122, 959–982, 1996.; Ringler, T. D., Thuburn, J., Klemp, J. B., and Skamarock, W. C.: A unified approach to energy conservation and potential vorticity dynamics for arbitrarily structured C-grids, J. Comput. Phys., 229, 3065–3090, 2010.; Ronchi, C., Iacono, R., and Paolucci, P. S.: The cubed sphere: a new method for the solution of partial differential equations in spherical geometry, J. Comput. Phys., 124, 93–114, 1996.; Salehipour, H., Stuhne, G. R., and Peltier, W. R.: A higher order

 
 



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