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

Miglena N. Koleva () and Lubin G. Vulkov
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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

Mathematics, 2023, vol. 11, issue 9, 1-21

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.

Keywords: surface layer of atmosphere; Caputo derivative; dispersion of pollutants; boundary degeneration; maximum principle; finite-difference scheme; positivity preserving (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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