��������������� Micro-scale Modelling: examination of two different approaches. Sarah-Jane Lock, Alison Coals, Alan Gadian and Stephen Mobbs NCAS, University of Leeds The presentation will examine:- 1. some of the latest approaches using the terrain following Gal Chen (and immersed boundary) approaches using preconditioning techniques .. (first 5 minutes of the talk) 2. Some of the latest work from Sarah-Jane Lock and Alison Coals, who prepared these later slides, with the cut cell devleopments .. (last 7 minutes of the talk) ��������������������� �
��������������������������������������������������������������������� For NWP and atmospheric modelling, grid point (finite difference) and spectral methods using some sort of Gal-Chen (height) or Sigma (pressure) co-ordinate systems have been dominant over the past 50 years. (Phillips, 1956, 2 level GCM model) There are now challenges to this status-quo, partly due to the advent of the rise of new engineering cfd approaches, and partly because essentially the atmospheric models have used a “vector” type approaches, which are not compatible with the “massively parallel” type architectures now being constructed. Different grid ideologies, such as hexagonal grids, unstructured grids are also knocking at the door. (ICON) Engineering (CFD) codes are being used to look at atmospheric flows (e.g. at Southampton) These are ideal for neutrally (i.e. unstratified) flows or heated (i.e . unstably stratified) flows. The argument has been, to date that perhaps they are not ideally suited to examine dispersive waves (i.e., stably stratified non-hydrostatic flow situations), which are found in the atmosphere, whether NWP or e.g. cloud process studies. The jury is still out (in my opinion!) The work at Leeds has examined the used of cut cell technology to represent the lower boundary. This has started with the work of David Woodhead (& Stephen Mobbs), and more recently with Sarah-Jane Lock and Alison Coals ( and I ) This talk will look at results from the Smolarkiewicz model and the cut cell work. ��������������������� �
�������������������������������������������������� ������� There are questions, whether with good newer iterative methods, for the Helmholtz equation, and even with terrain following co-ordinate system, results can be obtained which are good. ��������������������� �
"���������������������� Set-up for Gillygate experiment: (Dixon et al, 2005, Atmos Env ) Plan of Gillygate, York - Dashed outline defines the model domain. Two lamp-posts G3 and G4 are marked on the diagram These results use the Smolarkiewicz model, 256 processors on HPCx � periodic domain, with uniform z0 = 0.1m � grid-boxes: 231 x 261 x 60, for dx = dy = dz = 1m � time: 1200 time steps, for dt = 0.025s � model spin up ~ 30s - results computed for 30s run time – it is anticipated that the spin up and run times need to be longer for statistically significant outputs � Rayleigh damping sponge above 50m � Neutral, (constant potential temperature), u0= 5ms-1 from right to left. The periodic boundaries develop a logarithmic type surface layer ��������������������� !
���������#�����$�������%�������� ������������� Upper left frame is Vertical velocity. All other frames are concentra- tions. The two lamp-posts are marked. ��������������������� �
Exploring a cut-cell approach for model simulations of flow over hills in a microscale model S. Lock, A. Coals, A. Gadian University of Leeds With particular thanks to H.-W. Bitzer, U. Schaettler, J. Steppeler DWD, Germany ��������������������� &
������������������������������������������� • Background to cut-cell approach • Method(s) in the microscale model • Results from microscale model for idealised flows • Future work - microscale model and beyond! ��������������������� '
������������������� ������������� Adcroft, Marshall, Hill (1997): • explored shaved cells in representing irregular topography in an ocean model • 2 approaches: “partial steps” and “piecewise linear” (illustrated) • proposed a finite-volume approach to solve flow in shaved cells • solved 2D Boussinesq equations in flux-form => Gauss’s divergence theorem applied to fluxes in a (grid) volume • concluded piecewise linear gives a superior Figure taken from Adcroft et al. (1999 representation, especially at course resolutions ��������������������� (
���������� ������ • equation set: 3D, Cartesian, nonhydrostatic, fully compressible • prognostic/diagnostic variables • time-stepping: time-splitting method • numerical schemes: fully explicit (horizontal & vertical) 2 nd -order leapfrog 2 nd -order centred spatial • grid: Arakawa-C (horizontal) Charney-Phillips (vertical) • lower boundary: COSMO-DE cut-cell approach ��������������������� )
���������� ������ Prognostic variables: • equation set: u 3D, Cartesian, nonhydrostatic, v wind velocity fully compressible w • prognostic/diagnostic variables π ’ Exner pressure pert. θ ’ potential temp. pert. • time-stepping: q ( moist version) time-splitting method • numerical schemes: Diagnostic variables: fully explicit (horizontal & vertical) density ρ 2 nd -order leapfrog Exner pressure field Π 2 nd -order centred spatial potential temp. Θ p pressure • grid: Arakawa-C (horizontal) T in situ temperature Charney-Phillips (vertical) • lower boundary: COSMO-DE cut-cell approach ��������������������� �*
���������� ������ Based on Klemp & Wilhelmson (1978): • equation set: 3D, Cartesian, nonhydrostatic, Equations take the form fully compressible • prognostic/diagnostic variables where s φ = fast modes • time-stepping: f φ = slow modes time-splitting method Update slow modes on • numerical schemes: n long time-step ( ∆ t )… fully explicit (horizontal & vertical) 2 nd -order leapfrog 2 nd -order centred spatial …and fast modes • grid: Arakawa-C (horizontal) on intermediate n+1 short steps ( ∆ τ ) Charney-Phillips (vertical) • lower boundary: COSMO-DE cut-cell approach ��������������������� ��
���������� ���������������� �����������!���"� 0 (as in KW78) LHS = fast modes: RHS = slower modes: acoustic & gravity inc. advection, Coriolis, … Fast/slow mode split - as for COSMO & WRF models, & Cullen (1990) ��������������������� ��
���������� ������ Time-differencing: • equation set: 3D, Cartesian, nonhydrostatic, fully compressible For the long step, t - ∆ t 2 nd -order leapfrog • prognostic/diagnostic variables • time-stepping: time-splitting method inc. Robert-Asselin filter • numerical schemes: t For the short step, fully explicit (horizontal & vertical) 1 st -order forward- 2 nd -order leapfrog backward 2 nd -order centred spatial • grid: Arakawa-C (horizontal) t + ∆ t Charney-Phillips (vertical) • lower boundary: COSMO-DE cut-cell approach ��������������������� ��
���������� ������ Arakawa-C grid (horizontal): • equation set: 3D, Cartesian, nonhydrostatic, y fully compressible • prognostic/diagnostic variables x • time-stepping: time-splitting method Charney-Phillips grid (vertical): • numerical schemes: fully explicit (horizontal & vertical) 2 nd -order leapfrog z 2 nd -order centred space • grid: Arakawa-C (horizontal) x Charney-Phillips (vertical) • lower boundary: COSMO-DE cut-cell approach ��������������������� �!
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