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Vertical Discretization (vertical + discretization)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Vertical discretizations giving optimal representation of normal modes: Sensitivity to the form of the pressure-gradient term

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 621 2006
J. Thuburn
Abstract The normal-mode dispersion properties and structures of some vertical discretizations of the compressible Euler equations are re-examined. It is shown that the dispersion properties can be sensitive to the form in which the pressure-gradient term is expressed. For a height coordinate and for an isentropic vertical coordinate, discretizations are identified that have optimal dispersion properties and, at the same time, lend themselves to mass conservation by predicting the relevant density variable. Copyright © 2006 Royal Meteorological Society [source]

Appropriate vertical discretization of Richards' equation for two-dimensional watershed-scale modelling

HYDROLOGICAL PROCESSES, Issue 1 2004
Charles W. Downer
Abstract A number of watershed-scale hydrological models include Richards' equation (RE) solutions, but the literature is sparse on information as to the appropriate application of RE at the watershed scale. In most published applications of RE in distributed watershed-scale hydrological modelling, coarse vertical resolutions are used to decrease the computational burden. Compared to point- or field-scale studies, application at the watershed scale is complicated by diverse runoff production mechanisms, groundwater effects on runoff production, runon phenomena and heterogeneous watershed characteristics. An essential element of the numerical solution of RE is that the solution converges as the spatial resolution increases. Spatial convergence studies can be used to identify the proper resolution that accurately describes the solution with maximum computational efficiency, when using physically realistic parameter values. In this study, spatial convergence studies are conducted using the two-dimensional, distributed-parameter, gridded surface subsurface hydrological analysis (GSSHA) model, which solves RE to simulate vadose zone fluxes. Tests to determine if the required discretization is strongly a function of dominant runoff production mechanism are conducted using data from two very different watersheds, the Hortonian Goodwin Creek Experimental Watershed and the non-Hortonian Muddy Brook watershed. Total infiltration, stream flow and evapotranspiration for the entire simulation period are used to compute comparison statistics. The influences of upper and lower boundary conditions on the solution accuracy are also explored. Results indicate that to simulate hydrological fluxes accurately at both watersheds small vertical cell sizes, of the order of 1 cm, are required near the soil surface, but not throughout the soil column. The appropriate choice of approximations for calculating the near soil-surface unsaturated hydraulic conductivity can yield modest increases in the required cell size. Results for both watersheds are quite similar, even though the soils and runoff production mechanisms differ greatly between the two catchments. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Non-hydrostatic 3D free surface layer-structured finite volume model for short wave propagation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
L. Cea
Abstract In this paper a layer-structured finite volume model for non-hydrostatic 3D environmental free surface flow is presented and applied to several test cases, which involve the computation of gravity waves. The 3D unsteady momentum and mass conservation equations are solved in a collocated grid made of polyhedrons, which are built from a 2D horizontal unstructured mesh, by just adding several horizontal layers. The mesh built in such a way is unstructured in the horizontal plane, but structured in the vertical direction. This procedure simplifies the mesh generation and at the same time it produces a well-oriented mesh for stratified flows, which are common in environmental problems. The model reduces to a 2D depth-averaged shallow water model when one single layer is defined in the mesh. Pressure,velocity coupling is achieved by the Semi-Implicit Method for Pressure-Linked Equations algorithm, using Rhie,Chow interpolation to stabilize the pressure field. An attractive property of the model proposed is the ability to compute the propagation of short waves with a rather coarse vertical discretization. Several test cases are solved in order to show the capabilities and numerical stability of the model, including a rectangular free oscillating basin, a radially symmetric wave, short wave propagation over a 1D bar, solitary wave runup on a vertical wall, and short wave refraction over a 2D shoal. In all the cases the numerical results are compared either with analytical or with experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Sigma transformation and ALE formulation for three-dimensional free surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009
A. Decoene
Abstract In this paper we establish a link between the sigma transformation approach and the arbitrary Lagrangian,Eulerian (ALE) approach. For that purpose we introduce the ALE-sigma (ALES) approach, which consists in an ALE interpretation of the sigma transformation. Taking advantage of this new approach, we propose a general ALES transformation, allowing for a great adaptability of the vertical discretization and therefore overcoming some drawbacks of the classical sigma transformation. Numerical results are presented, showing the advantages of this general coordinate system, as, for example, a better representation of horizontal stratifications. Copyright © 2008 John Wiley & Sons, Ltd. [source]

A finite-element scheme for the vertical discretization of the semi-Lagrangian version of the ECMWF forecast model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 599 2004
A. Untch
Abstract A vertical finite-element (FE) discretization designed for the European Centre for Medium-Range Weather Forecasts (ECMWF) model with semi-Lagrangian advection is described. Only non-local operations are evaluated in FE representation, while products of variables are evaluated in physical space. With semi-Lagrangian advection the only non-local vertical operations to be evaluated are vertical integrals. An integral operator is derived based on the Galerkin method using B-splines as basis functions with compact support. Two versions have been implemented, one using piecewise linear basis functions (hat functions) and the other using cubic B-splines. No staggering of dependent variables is employed in physical space, making the method well suited for use with semi-Lagrangian advection. The two versions of the FE scheme are compared to finite-difference (FD) schemes in both the Lorenz and the Charney,Phillips staggering of the dependent variables for the linearized model. The FE schemes give more accurate results than the two FD schemes for the phase speeds of most of the linear gravity waves. Evidence is shown that the FE schemes suffer less from the computational mode than the FD scheme with Lorenz staggering, although temperature and geopotential are held at the same set of levels in the FE scheme too. As a result, the FE schemes reduce the level of vertical noise in forecasts with the full model. They also reduce by about 50% a persistent cold bias in the lower stratosphere present with the FD scheme in Lorenz staggering (i.e. the operational scheme at ECMWF before its replacement by the cubic version of the FE scheme described here) and improve the transport in the stratosphere. Copyright © 2004 Royal Meteorological Society [source]