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 128 articles , 1 standard article )

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  1. Capecelatro, Jesse: A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics (2018)
  2. Shankar, Varun; Wright, Grady B.: Mesh-free semi-Lagrangian methods for transport on a sphere using radial basis functions (2018)
  3. Subich, Christopher J.: Higher-order finite volume differential operators with selective upwinding on the icosahedral spherical grid (2018)
  4. Bosler, Peter A.; Kent, James; Krasny, Robert; Jablonowski, Christiane: A Lagrangian particle method with remeshing for tracer transport on the sphere (2017)
  5. Chun, S.; Eskilsson, C.: Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces (2017)
  6. Kang, Hyun-Gyu; Cheong, Hyeong-Bin: An efficient implementation of a high-order filter for a cubed-sphere spectral element model (2017)
  7. Allen, T.; Zerroukat, M.: A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid (2016)
  8. Chen, Qingshan: On staggering techniques and the non-staggered Z-grid scheme (2016)
  9. Chen, Sheng-Gwo; Wu, Jyh-Yang: Discrete conservation laws on evolving surfaces (2016)
  10. Gaudreault, Stéphane; Pudykiewicz, Janusz A.: An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere (2016)
  11. Peixoto, Pedro S.: Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative (2016)
  12. Townsend, Alex; Wilber, Heather; Wright, Grady B.: Computing with functions in spherical and polar geometries. I. The sphere (2016)
  13. 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)
  14. Behera, Ratikanta; Mehra, Mani; Kevlahan, N. K.-R.: Multilevel approximation of the gradient operator on an adaptive spherical geodesic grid (2015)
  15. Iga, Shin-ichi: Smooth, seamless, and structured grid generation with flexibility in resolution distribution on a sphere based on conformal mapping and the spring dynamics method (2015)
  16. Katta, Kiran K.; Nair, Ramachandran D.; Kumar, Vinod: High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme (2015)
  17. Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.: Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE (2015)
  18. Pereverzyev, S. V.; Sloan, I. H.; Tkachenko, P.: Parameter choice strategies for least-squares approximation of noisy smooth functions on the sphere (2015)
  19. Rauser, Florian; Marotzke, Jochem; Korn, Peter: Ensemble-type numerical uncertainty information from single model integrations (2015)
  20. Thuburn, John; Cotter, Colin J.: A primal-dual mimetic finite element scheme for the rotating shallow water equations on polygonal spherical meshes (2015)

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