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 152 articles , 1 standard article )

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  1. Arpaia, Luca; Ricchiuto, Mario: Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes (2020)
  2. Baldauf, Michael: Discontinuous Galerkin solver for the shallow-water equations in covariant form on the sphere and the ellipsoid (2020)
  3. Beale, J. Thomas: Solving partial differential equations on closed surfaces with planar Cartesian grids (2020)
  4. Eriksson, Anders; Nordmark, Arne: Computational stability investigations for a highly symmetric system: the pressurized spherical membrane (2020)
  5. Kang, Shinhoo; Giraldo, Francis X.; Bui-Thanh, Tan: IMEX HDG-DG: a coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for shallow water systems (2020)
  6. Shankar, Varun; Wright, Grady B.; Narayan, Akil: A robust hyperviscosity formulation for stable RBF-FD discretizations of advection-diffusion-reaction equations on manifolds (2020)
  7. Shashkin, Vladimir V.; Goyman, Gordey S.: Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid (2020)
  8. Wimmer, Golo A.; Cotter, Colin J.; Bauer, Werner: Energy conserving upwinded compatible finite element schemes for the rotating shallow water equations (2020)
  9. Beljadid, Abdelaziz; LeFloch, Philippe G.; Mohammadian, Abdolmajid: Late-time asymptotic behavior of solutions to hyperbolic conservation laws on the sphere (2019)
  10. Bendall, Thomas M.; Cotter, Colin J.; Shipton, Jemma: The `recovered space’ advection scheme for lowest-order compatible finite element methods (2019)
  11. Bosler, Peter A.; Bradley, Andrew M.; Taylor, Mark A.: Conservative multimoment transport along characteristics for discontinuous Galerkin methods (2019)
  12. Hamon, François P.; Schreiber, Martin; Minion, Michael L.: Multi-level spectral deferred corrections scheme for the shallow water equations on the rotating sphere (2019)
  13. Hoang, Thi-Thao-Phuong; Leng, Wei; Ju, Lili; Wang, Zhu; Pieper, Konstantin: Conservative explicit local time-stepping schemes for the shallow water equations (2019)
  14. Luan, Vu Thai; Pudykiewicz, Janusz A.; Reynolds, Daniel R.: Further development of efficient and accurate time integration schemes for meteorological models (2019)
  15. Peixoto, Pedro S.; Schreiber, Martin: Semi-Lagrangian exponential integration with application to the rotating shallow water equations (2019)
  16. Bauer, W.; Cotter, C. J.: Energy-enstrophy conserving compatible finite element schemes for the rotating shallow water equations with slip boundary conditions (2018)
  17. Budd, Chris J.; McRae, Andrew T. T.; Cotter, Colin J.: The scaling and skewness of optimally transported meshes on the sphere (2018)
  18. Capecelatro, Jesse: A purely Lagrangian method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics (2018)
  19. Korn, Peter; Linardakis, Leonidas: A conservative discretization of the shallow-water equations on triangular grids (2018)
  20. Lee, D.; Palha, A.: A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere (2018)

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