Numerical method for space degenerate fractional derivative problems of atmospheric pollution

Koleva, Miglena N.

doi:10.1063/5.0100645

Cited by 2 publications

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“…Fractional atmospheric models are introduced and analyzed in [3,[5][6][7][8]18,31]. In [3,5,6], the fractional differential equation in the longitudinal and vertical directions is used to derive the concentration distribution of pollutants in the PBL.…”

Section: Introductionmentioning

confidence: 99%

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

Koleva

Vulkov

2023

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

“…Ref. [31] constructs an exponential difference scheme for the fractional-order advectiondiffusion problem for the dispersion of pollutants with discontinuous diffusivity profiles. Ref.…”

Section: Introductionmentioning

confidence: 99%