New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Journal of Computational Physics
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
A parallel adaptive barotropic model of the atmosphere
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Short Note: A simple mass conserving semi-Lagrangian scheme for transport problems
Journal of Computational Physics
Journal of Computational Physics
Predicting goal error evolution from near-initial-information: A learning algorithm
Journal of Computational Physics
A discontinuous/continuous low order finite element shallow water model on the sphere
Journal of Computational Physics
A class of semi-implicit predictor-corrector schemes for the time integration of atmospheric models
Journal of Computational Physics
Hi-index | 31.49 |
A new class of unsteady analytical solutions of the spherical shallow water equations (SSWE) is presented. Analytical solutions of the SSWE are fundamental for the validation of barotropic atmospheric models. To date, only steady-state analytical solutions are known from the literature. The unsteady analytical solutions of the SSWE are derived by applying the transformation method to the transition from a fixed cartesian to a rotating coordinate system. Fundamental examples of the new unsteady analytical solutions are presented for specific wind profiles. With the presented unsteady analytical solutions one can provide a measure of the numerical convergence in the case of a temporally evolving system. An application to the atmospheric model PLASMA shows the benefit of unsteady analytical solutions for the quantification of convergence properties.