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Diffusion Scheme (diffusion + scheme)

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Engineering	28%

Selected Abstracts

Comparing vortex methods and finite difference methods in a homogeneous turbulent shear flow

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010
R. Yokota
Abstract The vortex method is applied to the calculation of a homogeneous shear turbulence, and compared with a finite difference code using identical calculation conditions. The core spreading method with spatial adaptation is selected as the viscous diffusion scheme of the vortex method. The shear rate is chosen so that it matches the maximum value observed in a fully developed channel flow. The isosurface, anisotropy tensors, and joint probability density functions reflect the ability of the present vortex method to quantitatively reproduce the anisotropic nature of strongly sheared turbulence, both instantaneously and statistically. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Semi-Lagrangian advection scheme with controlled damping: An alternative to nonlinear horizontal diffusion in a numerical weather prediction model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 631 2008
Filip Vá
Abstract This paper proposes a nonlinear horizontal diffusion scheme for models using semi-Lagrangian formulations. The scheme is made flow dependent and not entirely linked to the model levels. As an extension, the implementation of the scheme to the model Aladin is given. The damping abilities of interpolation are used for the diffusion filtering. The aim is to provide a horizontal diffusion scheme of similar stability and computational efficiency as the existing linear spectral diffusion scheme in Aladin. Preserving such qualities, the new scheme brings beneficial new skills to the model. The differences between the performances of the two diffusion schemes are examined and discussed. Finally, some interesting case-studies simulated with both horizontal diffusion schemes are presented. Copyright © 2008 Royal Meteorological Society [source]

Entropy sources in a dynamical core atmosphere model

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 614 2006
Tim Woollings
Abstract Numerical atmosphere models are not generally constructed to ensure accurate treatment of entropy, but little is known about the significance of the resulting errors. This paper examines the entropy changes during a baroclinic wave simulation in a typical dynamical core model, specifically a ,-coordinate spectral model, which includes scale-selective dissipation terms in the form of a numerical hyperdiffusion. Lagrangian entropy conservation is found to be badly represented, with numerical transport errors resulting in cross-isentrope mass fluxes which are of the same size as those associated with some real diabatic processes. In a global average, the total entropy increases at a rate of just 0.5 mW m,2K,1. This, however, is seen to be the residual of two opposing numerical effects which are several times larger, namely the destruction of entropy by dispersion and Gibbs errors, and its creation by diffusion. The entropy generated by diffusion is shown to be remarkably insensitive to the details of the diffusion scheme. This leads us to hypothesize that the entropy source from diffusion is determined by the rate at which small scales are generated by the deformation field of the large-scale flow so that, while the diffusion mechanism is clearly unrealistic, the magnitude of the entropy source is, we argue, representative of that generated by physical dissipative processes in the real atmosphere. Even in this simple model it is not possible to quantify precisely the different entropy sources and sinks which combine to give the overall entropy change. However, we can say that if there is a systematic spurious entropy source in this model, then it is small, i.e. of size 0.5 mW m,2K,1 or smaller. Copyright © 2006 Royal Meteorological Society [source]

The ECMWF operational implementation of four-dimensional variational assimilation.

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 564 2000
II: Experimental results with improved physics
Abstract A comprehensive set of physical parametrizations has been linearized for use in the European Centre for Medium-Range Weather Forecasts (ECMWF's) incremental four-dimensional variational (4D-Var) system described in Part I. The following processes are represented: vertical diffusion, subgrid-scale orographic effects, large-scale precipitation, deep moist convection and long-wave radiation. The tangent-linear approximation is examined for finite-size perturbations. Significant improvements are illustrated for surface wind and specific humidity with respect to a simplified vertical diffusion scheme. Singular vectors computed over 6 hours (compatible with the 4D-Var assimilation window) have lower amplification rates when the improved physical package is included, due to a more realistic description of dissipative processes, even though latent-heat release contributes to amplify the potential energy of perturbations in rainy areas. A direct consequence is a larger value of the observation term of the cost-function at the end of the minimization process when improved physics is included in 4D-Var. However, the larger departure of the analysis state from observations in the lower-resolution inner-loop is in better agreement with the behaviour of the full nonlinear model at high resolution. More precisely, the improved physics produces smaller discontinuities in the value of the cost-function when going from low to high resolution. In order to reduce the computational cost of the linear physics, a new configuration of the incremental 4D-Var system using two outer-loops is defined. In a first outer-loop, a minimization is performed at low resolution with simplified physics (50 iterations), while in the second loop a second minimization is performed with improved physics (20 iterations) after an update of the model trajectory at high resolution. In this configuration the extra cost of the physics is only 25%, and results from a 2-week assimilation period show positive impacts in terms of quality of the forecasts in the Tropics (reduced spin-down of precipitation, lower root-mean-square errors in wind scores). This 4D-Var configuration with improved physics and two outer-loops was implemented operationally at ECMWF in November 1997. [source]

Parallel simulation of unsteady hovering rotor wakes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2006
C. B. Allen
Abstract Numerical simulation using low diffusion schemes, for example free-vortex or vorticity transport methods, and theoretical stability analyses have shown the wakes of rotors in hover to be unsteady. This has also been observed in experiments, although the instabilities are not always repeatable. Hovering rotor wake stability is considered here using a finite-volume compressible CFD code. An implicit unsteady, multiblock, multigrid, upwind solver, and structured multiblock grid generator are presented, and applied to lifting rotors in hover. To allow the use of very fine meshes and, hence, better representation of the flow physics, a parallel version of the code has been developed, and parallel performance using upto 1024 CPUs is presented. A four-bladed rotor is considered, and it is demonstrated that once the grid density is sufficient to capture enough turns of the tip vortices, hover exhibits oscillatory behaviour of the wake, even using a steady formulation. An unsteady simulation is then performed, and also shows an unsteady wake. Detailed analysis of the time-accurate wake history shows that three dominant unsteady modes are captured, for this four-bladed case, with frequencies of one, four, and eight times the rotational frequency. A comparison with theoretical stability analysis is also presented. Copyright © 2006 John Wiley & Sons, Ltd. [source]