Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media

Chernogorova, Tatiana P.; Koleva, Miglena N.; Vulkov, Lubin G.

doi:10.1016/j.amc.2020.125691

Cited by 3 publications

(5 citation statements)

References 18 publications

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“…In this section, we discuss a very important property of numerical discretization, including the maximum principle and unconditional positivity preservation [25,26,28,47,54].…”

Section: Properties Of the Numerical Schemementioning

confidence: 99%

“…The computational domain is represented by Ω and it is within ABL. Classical (integer-order) atmospheric dispersion problems both with constant and non-constant eddy diffusivity and wind speed profiles are well studied in the literature [1,4,11,[13][14][15][16][22][23][24][25][26][27][28]. The effect of the boundary degeneration, arising from power-law modeling using the Monin-Obukhov [29] similarity theory and its impact on the accuracy of the numerical solution, is not sufficiently investigated.…”

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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“…In this section, we discuss a very important property of numerical discretization, including the maximum principle and unconditional positivity preservation [25,26,28,47,54].…”

Section: Properties Of the Numerical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Koleva

Vulkov

2023

Mathematics

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“…Their modification that is modified van Genuchten, with appropriate parameters 1 m , 1 n , 2 m , and 2 n , in Eq. ( 10) and (11). The curve-fitting parameters were increased from 3 to 6.…”

Section: The Problem Of Transition Between Constitutive Equationsmentioning

confidence: 99%

“…The intention of the modification was to increase the ability of the Eq. ( 10) and (11) to have a better curve-fitting ability than Eq. ( 7) and (8).…”

Section: The Problem Of Transition Between Constitutive Equationsmentioning

confidence: 99%

“…Richards' equation consists of a governing equation that is used to describe the water flow in subsurface porous media such as soil in unsaturated conditions [1]. It is continuously subjected to numerical investigation [2][3][4][5][6][7][8][9][10][11]. The modeling of water distribution using the equation has essential applications in climate science, agriculture and also ecosystem management [12].…”

Section: Introductionmentioning

confidence: 99%

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Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil: Numerical Simulations

Giap

Noborio

2021

ARFMTS

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Richards’ partial differential equation normally governs water flows in soil. It can be utilized to investigate water infiltration in the soil. A case study of the Haverkamp’s water infiltration simulation into Yolo Light Clay was carried out. A common practice to change between the hydraulic functions (from Haverkamp to van Genuchten) could cause a discrepancy in the simulation results. Hence, the first objective is to modify van Genuchten’s equations to reproduce the water infiltration result that was obtained using the Haverkamp constitutive functions. The method used was able to recreate water infiltration by increasing the fitting parameters of the van Genuchten constitutive functions. The second objective is to identify the mechanism governing the flow of water. The soil water diffusivity and the hydraulic conductivity were responsible for the flux of water in the soil. The Richards’ equation was discretized using a finite difference method, and the algebraic solution was coded into Simply Fortran 2008.

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Numerical method for space degenerate fractional derivative problems of atmospheric pollution

Koleva¹

2022

“TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Ann

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Exponential finite difference scheme for transport equations with discontinuous coefficients in porous media

Cited by 3 publications

References 18 publications

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

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

Transition Between Constitutive Equations and the Mechanics of Water Flow in Unsaturated Soil: Numerical Simulations

Numerical method for space degenerate fractional derivative problems of atmospheric pollution

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