Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Monomial cubature rules since “Stroud”: a compilation
Journal of Computational and Applied Mathematics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Lagrange-Galerkin methods on spherical geodesic grids
Journal of Computational Physics
From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex
SIAM Journal on Numerical Analysis
New icosahedral grid-point discretizations of the shallow water equations on the sphere
Journal of Computational Physics
Monomial cubature rules since “Stroud”: a compilation—part 2
Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Shallow water model on a modified icosahedral geodesic grid by using spring dynamics
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Two Barriers on Strong-Stability-Preserving Time Discretization Methods
Journal of Scientific Computing
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Journal of Computational Physics
A wave propagation algorithm for hyperbolic systems on curved manifolds
Journal of Computational Physics
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
International Journal of High Performance Computing Applications
Journal of Computational Physics
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
Unsteady analytical solutions of the spherical shallow water equations
Journal of Computational Physics
A parallel adaptive barotropic model of the atmosphere
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
SIAM Journal on Scientific Computing
A discontinuous/continuous low order finite element shallow water model on the sphere
Journal of Computational Physics
Journal of Computational Physics
Spurious inertial oscillations in shallow-water models
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
A global model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R^3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation which requires both area (elements) and line (element faces) integrals. Here, we use a Rusanov numerical flux to resolve the discontinuous fluxes at the element faces. A strong stability-preserving third-order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step. The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211-224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of O(@Dx^k^+^1) was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method limits the model error. Thus, the time step @Dt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.