Abstract
The advection scheme TRAP (from TRAPezium) was elaborated for the Bulgarian dispersion model EMAP, a PC-oriented Eulerian multi-layer model. The TRAP scheme is explicit, positively definite and conservative with limited numerical dispersion and good transportivity. Displaying the same properties as Bott’s scheme [1], the TRAP scheme turns out to be faster. In the Bott scheme the flux area is calculated by integrating the polynomial fit over the neighbouring grid values. In the TRAP scheme, the flux area is supposed trapezoidal. It is determined as a product of the Courant number and a single value of the approximating polynomial referring the middle of the passed distance. In the TRAP scheme, the same 4th order polynomial is used and Bott’s normalisation is also applied.
Some new and faster schemes build on the base of the TRAP concepts are presented and tested here. The performance quality is determined exploiting the rotational test: instantaneous point-shaped and cone-shaped sources are rotated in a 101x101 grid-point field. A set of criteria is used reflecting suitable characteristics of the advection algorithm. Additional demonstration tests are made over one of the schemes found out to be the best one.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bott, A. (1989), A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes, Mon.Wea.Rev. 117, pp. 1006–1015.
Bott, A. (1992), Monotone flux limitation in the area preserving flux form advection algorithm, Mon. Wea. Rev. 120, pp. 2592–2602.
Bott, A. (1993), The Monotone Area-preserving Flux-Form Advection Algorithm: Reducing the Time-splitting Error in Two-Dimensional Flow Fields, Mon.Wea.Rev. 121, 2637–2641.
Peters, L. K., Berkowitz, C. M., Carmichael, G. R., Easter, R. C., Fairweather, G., Ghan, S. J., Hales, J. M., Leung, L. R., Pennell, W. R., Potra, F. A., Saylor, R. D. and Tsang, T. T. (1995), The current state and future direction of Eulerian models in simulation the tropospheric chemistry and transport of trace species: a review, Atmos. Environ., 29, pp. 189–222.
Rood, R. B. (1987), Numerical advection algorithms and their role in atmospheric transport and chemistry models, Rev. Geophys. 25, pp. 71–100.
Smolarkiewiecz, P. K. (1982), The multidimensional Crowley advection scheme, Mon. Wea.Rev. 113, pp. 1109–1130.
Staniforth, A., Côté, J. and Pudikiewicz, J. (1978), Comments on “Smolarkiewicz’s deformational flow”, Mon.Wea.Rev. 115, pp. 894–900.
Syrakov, D. (1995), On a PC-oriented Eulerian Multi-Level Model for Long-Term Calculations of the Regional Sulphur Deposition, in S. E. Gryning and F. A. Schiermeier (eds.), Air Pollution Modelling and its Application XI, NATO • Challenges of Modern Society 21, Plenum Press, New York and London, pp. 645–646.
Syrakov, D. (1996), On the TRAP advection scheme - Description, tests and applications, in G. Geernaert, A. WallOe-Hansen and Z. Zlatev (eds.), Regional Modelling of Air Pollution in Europe. Proceedings of the first REMAPE Workshop, Copenhagen, Denmark, September 1996, National Environmental Research Institute, Denmark, pp. 141–152.
Syrakov, D. and Galperin, M. (1997) On a new Bott-type advection scheme and its further improvement, in H. Hass and I. J. Ackermann (eds.), Proc. of the first GLOREAM Workshop,Aachen, Germany, September 1997, Ford Forschungszentrum Aachen, pp. 103–109.
Tremback, C. J., Powell, J., Cotton, W. R. and Pielke, R. A. (1987), The forward-in-time upstream advection scheme: Extension to higher orders, Mon.Wea.Rev. 115, pp. 540–555.
WMO-TCSU (1979), Numerical methods used in atmospheric models, Vol. I and II, GARP Publication series, No 17.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Syrakov, D., Galperin, M. (1999). On Some Flux-Type Advection Schemes for Dispersion Modelling Application. In: Zlatev, Z., et al. Large Scale Computations in Air Pollution Modelling. NATO Science Series, vol 57. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4570-1_27
Download citation
DOI: https://doi.org/10.1007/978-94-011-4570-1_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5678-3
Online ISBN: 978-94-011-4570-1
eBook Packages: Springer Book Archive