Lagrange-Galerkin methods on spherical geodesic grids
Journal of Computational Physics
New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations
Journal of Computational Physics
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
An optimization of the Icosahedral grid modified by spring dynamics
Journal of Computational Physics
Journal of Computational Physics
Numerical solution of the reaction-advection-diffusion equation on the sphere
Journal of Computational Physics
Unsteady analytical solutions of the spherical shallow water equations
Journal of Computational Physics
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An edge-based unstructured mesh discretisation in geospherical framework
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A class of semi-implicit predictor-corrector schemes for the time integration of atmospheric models
Journal of Computational Physics
Improved smoothness and homogeneity of icosahedral grids using the spring dynamics method
Journal of Computational Physics
Hi-index | 31.47 |
The shallow water equations coupled to the set of reaction-advection-diffusion equations are discretized on a geodesic icosahedral mesh using the finite volume technique. The method of solution of this coupled system is based on the principle of semi-discretization. The algorithm is mass conserving and stable for advection with the Courant numbers up to 2.7. The important part of the methodology is the optimization of the node positions in the icosahedral grid. It is shown that a slight adjustment of the mesh is instrumental in improving the accuracy of the numerical approximation. The convergence of the approximation of the differential operators is evaluated and compared to the data published in the literature. Numerical tests performed with the shallow water solver include two advection experiments, steady and unsteady zonal balanced flow, mountain flow, and the Rossby wave. The mountain flow and the Rossby wave cases are used to test the transport properties of the method in the case of both passive and reactive scalar fields. The investigation of essential numerical characteristics of the method is concluded by the simulation of an unstable zonal jet. The numerical simulation is performed using the set of shallow water equations without dissipation as well as with the viscosity term added to the momentum equation. Results show that the behavior of the model is consistent with both the literature published on the subject and the general empirical evidence.