Abstract
Mathematical modeling of pollutant propagation in the air of coastal regions is considered. A new mathematical model of aerodynamic processes is proposed that takes into account a multitude of factors acting in coastal regions, such as high air humidity, variability of the air pressure and temperature, etc. Algorithms for the investigation of this model are developed and their software implementation is described.
Similar content being viewed by others
References
A. S. Monin and A. M. Yaglom, “On the laws of small-scale turbulent motion of fluids.,” Usp. Mat. Nauk 18 (5), 93–114 (1963).
G. I. Marchuk, Mathematical Simulation for Environmental Problems (Nauka, Moscow, 1982).
A. E. Aloyan, Dymanics and Kinetics of Gaseous Pollutants and Aerosols in Atmosphere: Course of Lectures (Institut Vychislitel,noi Matematiki, Ross. Akad Nauk, Moscow, 2002) [in Russian].
B. N. Chetverushkin and E. V. Shil’nikov, “Software package for 3D viscous gas flow simulation on multipro-cessor computer systems,” Comput. Math. Math. Phys. 48, 295–305 (2008).
A. A. Davydov, B. N. Chetverushkin, and E. V. Shil’nikov, “Simulating flows of incompressible and weakly com-pressible fluids on multicore hybrid computer systems,” Comput. Math. Math. Phys. 50, 2157–2165 (2010).
B. N. Chetverushkin, “Resolution limits of continuous media mode and their mathematical formulations,” Math. Models Comput. Simul. 5, 266–279 (2013).
K. A. Beklemysheva, I. B. Petrov, and A. V. Favorskaya, “Numerical simulation of processes in solid deformable media in the presence of dynamic contacts using the grid-characteristic method,” Math. Models Comput. Simul. 6, 294–304 (2014).
I. B. Petrov, A. V. Favorskaya, A. V. Sannikov, and I. E. Kvasov, “Grid characteristic method using high-order interpolation on tetrahedral hierarchical meshes with a multiple time step,” Math. Models Comput. Simul. 5, 409–415 (2013).
M. V. Muratov and I. B. Petrov, “Estimation of wave responses from subvertical macrofracture systems using a grid characteristic method,” Math. Models Comput. Simul. 25, 479–491 (2013).
A. I. Sukhinov, A. E. Chistyakov, and D. S. Khachunts, “Mathematical modeling of a multicomponent air medium motion and transfer of pollutants,” Izv. Yuzh. Feder. Univ., Tekhn. Nauki, No. 8, 73–79 (2011).
A. I. Sukhinov, A. E. Chistyakov, and E. A. Protsenko, “Mathematical modeling of sediment transport in the coastal zone of shallow reservoirs,” Math. Models Comput. Simul. 5, 351–363 (2013).
O. M. Belotserkovskii, V. A. Gushchin, and V. V. Shchennikov, “The splitting method as applied to the dynamics of viscous incompressible fluid,” Zh. Vychisl. Mat. Mat. Fiz. 15 (1), 197–207 (1975).
V. A. Gushchin and P. V. Matyushin, “Numerical simulation and visualization of vortical structure transformation in the flow past a sphere at an increasing degree of stratification,” Comput. Math. Math. Phys. 51, 251–263 (2011).
A. I. Sukhinov, A. E. Chistyakov, and A. V. Shishenya, “Error estimate for diffusion equations solved by schemes with weights,” Math. Models Comput. Simul. 26, 324–331 (2014).
A. I. Sukhinov, A. E. Chistyakov, and N. A. Fomenko, “A procedure for constructing difference schemes for the diffusion–convection–reaction problem with account for population of control cells,” Izv. Yuzh. Feder. Univ., Tekhn. Nauki, No. 4, 87–98 (2013).
A. I. Sukhinov, A. E. Chistyakov, E. F. Timofeeva, and A. V. Shishenya, “Mathematical model for calculating coastal wave processes,” Math. Models Comput. Simul. 25, 122–129 (2013).
A. I. Sukhinov and D. S. Khachunts, “Software implementation of a two-dimensional air motion problem,” Izv. Yuzh. Feder. Univ., Tekhn. Nauki, No. 4, 15–20 (2013).
A. E. Chistyakov and D. S. Khachunts, “The prolem of multicomponent air medium motion with regard to steam generation and condensation,” Izv. Yuzh. Feder. Univ., Tekhn. Nauki, No. 4, 87–98 (2013).
A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).
A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations (Nauka, Moscow, 1978; Birkhäuser, Basel, 1989).
A. N. Konovalov, “The steepest descent method with an adaptive alternating-triangular preconditioner,” Differ. Equations 40, 1018–1028 (2004).
A. N. Konovalov, “On the theory of alternating-triangular iterative method,” Sib. Mat. Zh. 43 (3), 552 (2002).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.I. Sukhinov, D.S. Khachunts, A.E. Chistyakov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 7, pp. 1238–1254.
Rights and permissions
About this article
Cite this article
Sukhinov, A.I., Khachunts, D.S. & Chistyakov, A.E. A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation. Comput. Math. and Math. Phys. 55, 1216–1231 (2015). https://doi.org/10.1134/S096554251507012X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S096554251507012X