The Experts below are selected from a list of 23850 Experts worldwide ranked by ideXlab platform
Jan Verwer - One of the best experts on this subject based on the ideXlab platform.
-
Spatial Discretization of the shallow water equations in spherical geometry using osher s scheme
Journal of Computational Physics, 2000Co-Authors: D. Lanser, Joke Blom, Jan VerwerAbstract:Abstract The shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models. Since the seventies these models have often been solved with spectral methods. Increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods. In this paper we study the use of Osher's finite-volume scheme for the Spatial Discretization of the shallow water equations on the rotating sphere. This finite volume scheme of upwind type is well suited for solving a hyperbolic system of equations. Special attention is paid to the pole problem. To that end Osher's scheme is applied on the common (reduced) latitude-longitude grid and on a stereographic grid. The latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist. The latitude-longitude grid is preferred on lower latitudes. Therefore, across the sphere we apply Osher's scheme on a combined grid connecting the two grids at high latitude. We will show that this provides an attractive Spatial Discretization for explicit integration methods, as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude-longitude grid only. When time step limitation plays no significant role, the standard (reduced) latitude-longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles.
-
Spatial Discretization of the shallow water equations in spherical geometryusing Osher's scheme
Report Modelling Analysis and Simulation, 1999Co-Authors: D. Lanser, Joke Blom, Jan VerwerAbstract:textabstractThe shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models. Since the seventies these models are often solved with spectral methods. Increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods. In this paper we study the use of Osher's finite-volume scheme for the Spatial Discretization of the shallow water equations on the rotating sphere. This high-order finite volume scheme of upwind type is well suited to solve a hyperbolic system of equations. Special attention is paid to the pole problem. To that end Osher's scheme is applied on the common (reduced) latitude-longitude grid and on a stereographic grid. The latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist. The latitude-longitude grid is preferred on lower latitudes. Therefore, across the sphere we apply Osher's scheme on a combined grid connecting the two grids at high latitude. We will show that this provides an attractive Spatial Discretization for explicit integration methods, as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude-longitude grid only. When time step limitation plays no significant role, the standard (reduced) latitude-longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles.
Paul Kotyczka - One of the best experts on this subject based on the ideXlab platform.
-
Structure preserving Spatial Discretization of 2D hyperbolic systems using staggered grids finite difference
2017 American Control Conference (ACC), 2017Co-Authors: Vincent Trenchant, Hector Ramirez, Yann Le Gorrec, Paul KotyczkaAbstract:This paper proposes a finite difference Spatial Discretization scheme that preserve the port-Hamiltonian structure of 1D and 2D infinite dimensional hyperbolic systems. This scheme is based on the use of staggered grids for the Discretization of the state and co state variables of the system. It is shown that, by an appropriate choice of the boundary port variables, the underlying geometric structure of the infinite-dimensional system, i.e. its Dirac structure, is preserved during the Discretization step. The consistency of the Spatial Discretization scheme is evaluated and its accuracy is validated with numerical results.
D. Lanser - One of the best experts on this subject based on the ideXlab platform.
-
Spatial Discretization of the shallow water equations in spherical geometry using osher s scheme
Journal of Computational Physics, 2000Co-Authors: D. Lanser, Joke Blom, Jan VerwerAbstract:Abstract The shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models. Since the seventies these models have often been solved with spectral methods. Increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods. In this paper we study the use of Osher's finite-volume scheme for the Spatial Discretization of the shallow water equations on the rotating sphere. This finite volume scheme of upwind type is well suited for solving a hyperbolic system of equations. Special attention is paid to the pole problem. To that end Osher's scheme is applied on the common (reduced) latitude-longitude grid and on a stereographic grid. The latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist. The latitude-longitude grid is preferred on lower latitudes. Therefore, across the sphere we apply Osher's scheme on a combined grid connecting the two grids at high latitude. We will show that this provides an attractive Spatial Discretization for explicit integration methods, as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude-longitude grid only. When time step limitation plays no significant role, the standard (reduced) latitude-longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles.
-
Spatial Discretization of the shallow water equations in spherical geometryusing Osher's scheme
Report Modelling Analysis and Simulation, 1999Co-Authors: D. Lanser, Joke Blom, Jan VerwerAbstract:textabstractThe shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models. Since the seventies these models are often solved with spectral methods. Increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods. In this paper we study the use of Osher's finite-volume scheme for the Spatial Discretization of the shallow water equations on the rotating sphere. This high-order finite volume scheme of upwind type is well suited to solve a hyperbolic system of equations. Special attention is paid to the pole problem. To that end Osher's scheme is applied on the common (reduced) latitude-longitude grid and on a stereographic grid. The latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist. The latitude-longitude grid is preferred on lower latitudes. Therefore, across the sphere we apply Osher's scheme on a combined grid connecting the two grids at high latitude. We will show that this provides an attractive Spatial Discretization for explicit integration methods, as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude-longitude grid only. When time step limitation plays no significant role, the standard (reduced) latitude-longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles.
Vincent Trenchant - One of the best experts on this subject based on the ideXlab platform.
-
Structure preserving Spatial Discretization of 2D hyperbolic systems using staggered grids finite difference
2017 American Control Conference (ACC), 2017Co-Authors: Vincent Trenchant, Hector Ramirez, Yann Le Gorrec, Paul KotyczkaAbstract:This paper proposes a finite difference Spatial Discretization scheme that preserve the port-Hamiltonian structure of 1D and 2D infinite dimensional hyperbolic systems. This scheme is based on the use of staggered grids for the Discretization of the state and co state variables of the system. It is shown that, by an appropriate choice of the boundary port variables, the underlying geometric structure of the infinite-dimensional system, i.e. its Dirac structure, is preserved during the Discretization step. The consistency of the Spatial Discretization scheme is evaluated and its accuracy is validated with numerical results.
Jeanfrancois Geleyn - One of the best experts on this subject based on the ideXlab platform.
-
importance of temporal symmetry in Spatial Discretization for geostrophic adjustment in semi implicit z grid schemes
Quarterly Journal of the Royal Meteorological Society, 2015Co-Authors: Steven Caluwaerts, Daan Degrauwe, Piet Termonia, Fabrice Voitus, Pierre Benard, Jeanfrancois GeleynAbstract:Among the dynamical cores of numerical weather prediction communities, many different Discretization methods can be distinguished to solve the equations governing the motions in the atmosphere numerically. One of them, the Z-grid approach, is based on solving the equations formulated in terms of divergence and vorticity on an Arakawa A-grid, a grid where all the variables are defined at the same grid points. To permit an efficient semi-implicit (SI) treatment, Z-grid schemes were proposed in the literature that first perform SI time Discretization on the momentum equations formulated in terms of velocity components in order to construct from this a discretized divergence equation. This publication shows that a careful formulation of such SI Z-grid schemes is required to conserve appropriate dispersion relations for inertia–gravity, inertia–Lamb and Rossby waves. It is proven analytically for a two time-level (2TL) SI Z-grid scheme of the 1D shallow-water equations that the Spatial Discretization must respect temporal symmetry, meaning that the Spatial Discretization must be identical in the implicit and explicit parts of the scheme. If not, the discretized waves are damped or amplified and their phase and group velocity may be seriously distorted. These findings are discussed in detail and both 1D and 2D numerical tests are carried out to demonstrate that a symmetric formulation is an important modelling constraint in order to obtain an appropriate geostrophic adjustment.
