A standard test set for numerical approximations to the shallow water equations in spherical geometry. The numerical methods devised by the authors for solving shallow water equations in spherical geometry are applied to seven test cases presented in order of complexity. The aim, of course, is to perfect a numerical method for climate modelling. The seven cases are as follows: (i) advection of cosine bell over the pole, (ii) steady nonlinear zonal geostrophic flow, (iii) nonlinear steady zonal geostrophic flow with compact support, (iv) forced nonlinear system with a translating low pressure centre, (v) zonal flow over an isolated mountain, (vi) Rossby-Haurwitz wave, and (vii) observed atmospheric states.

References in zbMATH (referenced in 109 articles , 1 standard article )

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  1. Chen, Qingshan: On staggering techniques and the non-staggered Z-grid scheme (2016)
  2. Chen, Sheng-Gwo; Wu, Jyh-Yang: Discrete conservation laws on evolving surfaces (2016)
  3. Townsend, Alex; Wilber, Heather; Wright, Grady B.: Computing with functions in spherical and polar geometries. I. The sphere (2016)
  4. Tumolo, Giovanni: A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals (2016)
  5. Behera, Ratikanta; Mehra, Mani; Kevlahan, N.K.-R.: Multilevel approximation of the gradient operator on an adaptive spherical geodesic grid (2015)
  6. Lott, P.Aaron; Woodward, Carol S.; Evans, Katherine J.: Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE (2015)
  7. Rauser, Florian; Marotzke, Jochem; Korn, Peter: Ensemble-type numerical uncertainty information from single model integrations (2015)
  8. Thuburn, John; Cotter, Colin J.: A primal-dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes (2015)
  9. Tillenius, Martin; Larsson, Elisabeth; Lehto, Erik; Flyer, Natasha: A scalable RBF-FD method for atmospheric flow (2015)
  10. Tregubov, I.; Tran, T.: A Galerkin method with spherical splines for the shallow water equations on a sphere: error analysis (2015)
  11. Zerroukat, M.; Allen, T.: A moist Boussinesq shallow water equations set for testing atmospheric models (2015)
  12. Bao, Lei; Nair, Ramachandran D.; Tufo, Henry M.: A mass and momentum flux-form high-order discontinuous Galerkin shallow water model on the cubed-sphere (2014)
  13. Cotter, C.J.; Thuburn, J.: A finite element exterior calculus framework for the rotating shallow-water equations (2014)
  14. Erath, Christoph; Nair, Ramachandran D.: A conservative multi-tracer transport scheme for spectral-element spherical grids (2014)
  15. Erath, Christoph; Nair, Ramachandran D.: Reprint of: A conservative multi-tracer transport scheme for spectral-element spherical grids (2014)
  16. Giesselmann, Jan; Müller, Thomas: Geometric error of finite volume schemes for conservation laws on evolving surfaces (2014)
  17. Iga, Shin-ichi; Tomita, Hirofumi: Improved smoothness and homogeneity of icosahedral grids using the spring dynamics method (2014)
  18. Mignone, A.: High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates (2014)
  19. Peixoto, Pedro S.; Barros, Saulo R.M.: On vector field reconstructions for semi-Lagrangian transport methods on geodesic staggered grids (2014)
  20. Shamir, Ofer; Paldor, Nathan: A Hermite-based shallow water solver for a thin “ocean” over a rotating sphere (2014)

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