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 168 articles , 1 standard article )

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  1. Bihlo, Alex; Popovych, Roman O.: Physics-informed neural networks for the shallow-water equations on the sphere (2022)
  2. Brachet, M.; Croisille, J.-P.: A center compact scheme for the shallow water equations on the sphere (2022)
  3. Capodaglio, Giacomo; Petersen, Mark: Local time stepping for the shallow water equations in MPAS (2022)
  4. Gaudreault, Stéphane; Charron, Martin; Dallerit, Valentin; Tokman, Mayya: High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid (2022)
  5. Betteridge, Jack; Gibson, Thomas H.; Graham, Ivan G.; Müller, Eike H.: Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations (2021)
  6. Biagioli, Elisa; de’ Michieli Vitturi, Mattia; Di Benedetto, Fabio: Modified shallow water model for viscous fluids and positivity preserving numerical approximation (2021)
  7. Goyman, Gordey S.; Shashkin, Vladimir V.: Horizontal approximation schemes for the staggered reduced latitude-longitude grid (2021)
  8. Maurya, Praveen K.; Yadav, Vivek S.; Mahato, Bikash; Ganta, Naveen; Rajpoot, Manoj K.; Bhumkar, Yogesh G.: New optimized implicit-explicit Runge-Kutta methods with applications to the hyperbolic conservation laws (2021)
  9. Meng, Xucheng; Hoang, Thi-Thao-phuong; Wang, Zhu; Ju, Lili: Localized exponential time differencing method for shallow water equations: algorithms and numerical study (2021)
  10. Wimmer, Golo A.; Cotter, Colin J.; Bauer, Werner: Energy conserving SUPG methods for compatible finite element schemes in numerical weather prediction (2021)
  11. Arpaia, Luca; Ricchiuto, Mario: Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes (2020)
  12. Baldauf, Michael: Discontinuous Galerkin solver for the shallow-water equations in covariant form on the sphere and the ellipsoid (2020)
  13. Beale, J. Thomas: Solving partial differential equations on closed surfaces with planar Cartesian grids (2020)
  14. Eriksson, Anders; Nordmark, Arne: Computational stability investigations for a highly symmetric system: the pressurized spherical membrane (2020)
  15. Gunderman, David; Flyer, Natasha; Fornberg, Bengt: Transport schemes in spherical geometries using spline-based RBF-FD with polynomials (2020)
  16. Hamon, François P.; Schreiber, Martin; Minion, Michael L.: Parallel-in-time multi-level integration of the shallow-water equations on the rotating sphere (2020)
  17. Holm, Håvard H.; Brodtkorb, André R.; Broström, Göran; Christensen, Kai H.; Sætra, Martin L.: Evaluation of selected finite-difference and finite-volume approaches to rotational shallow-water flow (2020)
  18. 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)
  19. Shankar, Varun; Wright, Grady B.; Narayan, Akil: A robust hyperviscosity formulation for stable RBF-FD discretizations of advection-diffusion-reaction equations on manifolds (2020)
  20. Shashkin, Vladimir V.; Goyman, Gordey S.: Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid (2020)

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