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 95 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. Behera, Ratikanta; Mehra, Mani; Kevlahan, N.K.-R.: Multilevel approximation of the gradient operator on an adaptive spherical geodesic grid (2015)
  5. Lott, P.Aaron; Woodward, Carol S.; Evans, Katherine J.: Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE (2015)
  6. Tregubov, I.; Tran, T.: A Galerkin method with spherical splines for the shallow water equations on a sphere: error analysis (2015)
  7. Giesselmann, Jan; Müller, Thomas: Geometric error of finite volume schemes for conservation laws on evolving surfaces (2014)
  8. Yang, Haijian; Yang, Chao; Cai, Xiao-Chuan: Parallel domain decomposition methods with mixed order discretization for fully implicit solution of tracer transport problems on the cubed-sphere (2014)
  9. Chen, Qingshan; Ringler, Todd; Gunzburger, Max: A co-volume scheme for the rotating shallow water equations on conforming non-orthogonal grids (2013)
  10. Croisille, Jean-Pierre: Hermitian compact interpolation on the cubed-sphere grid (2013)
  11. Tumolo, G.; Bonaventura, L.; Restelli, M.: A semi-implicit, semi-Lagrangian, $p$-adaptive discontinuous Galerkin method for the shallow water equations (2013)
  12. Chun, Sehun: Method of moving frames to solve conservation laws on curved surfaces (2012)
  13. Düben, Peter D.; Korn, Peter; Aizinger, Vadym: A discontinuous/continuous low order finite element shallow water model on the sphere (2012)
  14. Flyer, Natasha; Lehto, Erik; Blaise, Sébastien; Wright, Grady B.; St-Cyr, Amik: A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere (2012)
  15. Janakiraman, S.; Nanjundiah, Ravi S.; Vasudeva Murthy, A.S.: A novel variable resolution global spectral method on the sphere (2012)
  16. Sjögreen, Björn: High order finite difference and finite volume methods for advection on the sphere (2012)
  17. Tolstykh, Mikhail A.; Shashkin, Vladimir V.: Vorticity-divergence mass-conserving semi-Lagrangian shallow-water model using the reduced grid on the sphere (2012)
  18. Ullrich, Paul A.; Jablonowski, Christiane: MCore: a non-hydrostatic atmospheric dynamical core utilizing high-order finite-volume methods (2012)
  19. Archibald, Rick; Fann, George; Shelton, William: Adaptive discontinuous Galerkin methods in multiwavelets bases (2011)
  20. Flyer, Natasha; Fornberg, Bengt: Radial basis functions: developments and applications to planetary scale flows (2011)

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