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Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer

Author

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  • Miglena N. Koleva

    (Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria)

  • Lubin G. Vulkov

    (Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria)

Abstract

In this study, a numerical solution for degenerate space–time fractional advection–dispersion equations is proposed to simulate atmospheric dispersion in vertically inhomogeneous planetary boundary layers. The fractional derivative exists in a Caputo sense. We establish the maximum principle and a priori estimates for the solutions. Then, we construct a positivity-preserving finite-difference scheme, using monotone discretization in space and L1 approximation on the non-uniform mesh for the time derivative. We use appropriate grading techniques for the time–space mesh in order to overcome the boundary degeneration and weak singularity of the solution at the initial time. The computational results are demonstrated on the Gaussian fractional model as well on the boundary layers defined by height-dependent wind flow and diffusitivity, especially for the Monin–Obukhov model.

Suggested Citation

  • Miglena N. Koleva & Lubin G. Vulkov, 2023. "Numerical Solution of Fractional Models of Dispersion Contaminants in the Planetary Boundary Layer," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2040-:d:1132620
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    References listed on IDEAS

    as
    1. Goulart, A.G.O. & Lazo, M.J. & Suarez, J.M.S. & Moreira, D.M., 2017. "Fractional derivative models for atmospheric dispersion of pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 9-19.
    2. Chernogorova, Tatiana P. & Koleva, Miglena N. & Vulkov, Lubin G., 2021. "Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Ebru Ozbilge & Fatma Kanca & Emre Özbilge, 2022. "Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions," Mathematics, MDPI, vol. 10(9), pages 1-8, April.
    4. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2019. "A new parameterization for the concentration flux using the fractional calculus to model the dispersion of contaminants in the Planetary Boundary Layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 38-49.
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