Skip to main content
Log in

A mathematical model of pollutant propagation in near-ground atmospheric layer of a coastal region and its software implementation

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. 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).

    Google Scholar 

  2. G. I. Marchuk, Mathematical Simulation for Environmental Problems (Nauka, Moscow, 1982).

    Google Scholar 

  3. 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].

    Google Scholar 

  4. 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).

    Article  MathSciNet  Google Scholar 

  5. 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).

    Article  MathSciNet  Google Scholar 

  6. B. N. Chetverushkin, “Resolution limits of continuous media mode and their mathematical formulations,” Math. Models Comput. Simul. 5, 266–279 (2013).

    Article  MathSciNet  Google Scholar 

  7. 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).

    Article  Google Scholar 

  8. 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).

    Article  Google Scholar 

  9. 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).

    Article  MathSciNet  Google Scholar 

  10. 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).

    Google Scholar 

  11. 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).

    MathSciNet  MATH  Google Scholar 

  12. 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).

    Google Scholar 

  13. 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).

    Article  MathSciNet  Google Scholar 

  14. 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).

    Article  MathSciNet  Google Scholar 

  15. 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).

    Google Scholar 

  16. 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).

    Article  MathSciNet  Google Scholar 

  17. 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).

    Google Scholar 

  18. 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).

    Google Scholar 

  19. A. A. Samarskii, Theory of Finite Difference Schemes (Nauka, Moscow, 1989; Marcel Dekker, New York, 2001).

    Book  Google Scholar 

  20. A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations (Nauka, Moscow, 1978; Birkhäuser, Basel, 1989).

    Book  MATH  Google Scholar 

  21. A. N. Konovalov, “The steepest descent method with an adaptive alternating-triangular preconditioner,” Differ. Equations 40, 1018–1028 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  22. A. N. Konovalov, “On the theory of alternating-triangular iterative method,” Sib. Mat. Zh. 43 (3), 552 (2002).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Sukhinov.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S096554251507012X

Keywords

Navigation