Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media [PDF]
E3S Web of Conferences, 2022 The combined advection-diffusion-reaction (ADR) equation, which describe the transport problem of a contaminant in porous medium, does not generally admit an analytical solution.
El Arabi Inasse +2 more
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Porous Medium Equation with a Drift: Free Boundary Regularity [PDF]
Archive for Rational Mechanics and Analysis, 2021 39 pages, 1 ...
Kim, Inwon, Zhang, Yuming Paul
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Quenching for Porous Medium Equations
Tamkang Journal of Mathematics, 2021 This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as kt blows up at the same finite time and lower bound estimates of the quenching time of the equation kt = (kn)xx + (1 − k)−α, (x,t) ∈ (0,L) × (0,T) with (kn)x (0,t) = 0, (kn)x (L,t) = (
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Acoustics of Fractal Porous Material and Fractional Calculus
Mathematics, 2021 In this paper, we present a fractal (self-similar) model of acoustic propagation in a porous material with a rigid structure. The fractal medium is modeled as a continuous medium of non-integer spatial dimension.
Zine El Abiddine Fellah +4 more
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From Darcy Equation to Darcy Paradox
Fluids, 2022 This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach
Carmine Di Nucci, Daniele Celli
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Weak Solutions of the Porous Medium Equation [PDF]
Transactions of the American Mathematical Society, 1993 We show that if u ≥ 0 u \geq 0 , u ∈ L loc m ( Ω ) u \in L_{{\text {loc}}}^m(\Omega ) , Ω ⊂ R
Dahlberg, Björn E. J., Kenig, Carlos E.
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Modelling and simulation of waves in three-layer porous media [PDF]
Nonlinear Processes in Geophysics, 2013 The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a
S. R. Pudjaprasetya
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A Radó theorem for the porous medium equation [PDF]
Boletín de la Sociedad Matemática Mexicana, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dmitry Fedchenko, Nikolai Tarkhanov
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On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials
Entropy, 2019 We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory ...
Sergey Nazarenko +2 more
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The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow
Scientific Reports, 2022 Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling.
Rostislav Vodák +3 more
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