Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
A New Triangular Finite-Element with Optimum Constraint Ratio for Compressible Fluids
SIAM Journal on Scientific Computing
Dispersion Relation Analysis of the $P^NC_1 - P^_1$ Finite-Element Pair in Shallow-Water Models
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Dispersion Analysis of Discontinuous Galerkin Schemes Applied to Poincaré, Kelvin and Rossby Waves
Journal of Scientific Computing
SIAM Journal on Scientific Computing
A discontinuous Galerkin method for the shallow water equations in spherical triangular coordinates
Journal of Computational Physics
Kernel Analysis of the Discretized Finite Difference and Finite Element Shallow-Water Models
SIAM Journal on Scientific Computing
Numerical representation of geostrophic modes on arbitrarily structured C-grids
Journal of Computational Physics
Journal of Computational Physics
A simple finite volume method for the shallow water equations
Journal of Computational and Applied Mathematics
Numerical wave propagation for the triangular P1DG-P2 finite element pair
Journal of Computational Physics
Time Discretization Schemes for Poincaré Waves in Finite-Element Shallow-Water Models
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem. Indeed, the coupling between the momentum and the continuity equations usually leads to the appearance of spurious solutions and to anomalous dissipation/dispersion in the representation of the fast (Poincare) and slow (Rossby) waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier/dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. However, the cause of spurious oscillations and reduced convergence rates, that have been detected for most of mixed-order finite element shallow-water formulations, in simulating classical problems of geophysical fluid dynamics, is still an open question. The aim of the present study is to show that when spurious inertial solutions are present, they are mainly responsible for the aforementioned problems. Further, a criterion is found which determines the existence and the number of spurious inertial solutions. As it is delicate to cure spurious inertial modes, a class of possible discretization schemes is proposed, that is not affected by such spurious solutions.