Abstract:
A new method for constructing efficient monotone numerical schemes for solving direct, adjoint, and inverse atmospheric chemistry problems is presented. It is a systhesis of a variational principles combined with splitting and decomposition methods and a constructive realization of the Eulerian integrating factors (EIM) by means of the local adjoint problem technique. To provide the efficiency of calculations, a method to decompose the multi component substances transformation operators in terms of mechanisms of reactions is also proposed. With the analytical EIMs, the decomposed systems of stiff ODEs are reduced to the equivalent systems of integral equations. To solve them, non-iterative multistage algorithms of given order of accuracy are developed. An original variational method for constructing of mutually consistent algorithms for direct and adjoint problems, and sensitivity studies for complex models with constraints is developed.
Key words:
variational principle, stiff systems ODE, integrating multipliers, discrete-analytical approximations, atmospheric chemistry, algorithms for sensitivity studies.
Citation:
V. V. Penenko, E. A. Tsvetova, “Variational methods for constructing of monotone approximations for atmospheric chemistry models”, Sib. Zh. Vychisl. Mat., 16:3 (2013), 243–256; Num. Anal. Appl., 6:3 (2013), 210–220
This publication is cited in the following 7 articles:
V. V. Penenko, A. V. Penenko, E. A. Tsvetova, “Variational approach to the study of processes of geophysical hydro-thermodynamics with assimilation of observation data”, J. Appl. Mech. Tech. Phys., 58:5 (2017), 771–778
A. V. Penenko, A. A. Sorokovoy, K. E. Sorokovaya, “Numerical model of bioaerosol transformation in the atmosphere”, Atmos. Ocean. Opt., 29:6 (2016), 570–574
A. Penenko, P. Antokhin, “Numerical study of direct variational algorithm for assimilation of atmospheric chemistry data into transport and transformation model”, 22Nd International Symposium on Atmospheric and Ocean Optics: Atmospheric Physics, Proceedings of SPIE, 10035, eds. G. Matvienko, O. Romanovskii, Spie-Int Soc Optical Engineering, 2016, 100356F
Alexey Penenko, Pavel Antokhin, “Numerical study of variational data assimilation algorithms based on decomposition methods in atmospheric chemistry models”, IOP Conf. Ser.: Earth Environ. Sci., 48 (2016), 012021
Penenko V.V. Tsvetova E.A. Penenko A.V., “Methods Based on the Joint Use of Models and Observational Data in the Framework of Variational Approach To Forecasting Weather and Atmospheric Composition Quality”, Russ. Meteorol. Hydrol., 40:6 (2015), 365–373
Penenko V.V., Tsvetova E.A., Penenko A.V., “Development of Variational Approach For Direct and Inverse Problems of Atmospheric Hydrodynamics and Chemistry”, Izv. Atmos. Ocean. Phys., 51:3 (2015), 311–319
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