Advection–diffusion–absorption problem for microparticles in a porous layer with discrete boundary data
DOI:
https://doi.org/10.15407/fmmit2026.42.145Keywords:
концентрація, мікрочастинка, пористе тіло, дифузія, адвекція, абсорбція, неповні дані, метод оптимізаціїAbstract
The paper considers an advection–diffusion–absorption problem for microparticles in a porous layer under conditions where only discrete-in-time concentration values are specified on one of its boundaries. Such data are insufficient for the direct formulation of a well-posed initial-boundary value problem. To reconstruct a continuous boundary condition, a parametric family of approximation functions based on expressions typical of analytical solutions to advection–diffusion equations is proposed. An analytical solution of the one-dimensional advection–diffusion–absorption problem in a layer of constant thickness is obtained. The spatial-temporal distributions of microparticle concentration and their absorbed density, as well as the total accumulated mass of absorbed particles in the layer, are determined. An approach for estimating the time required to reach a critical absorption level, after which the constant-coefficient model may lose adequacy for describing the process, is proposed. Numerical analysis of approximation errors and convergence of the constructed solution is carried out.
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Copyright (c) 2026 Богдан Гера, Ольга Чернуха, Анастасія Чучвара, Юрій Білущак (Автор)
This work is licensed under a Creative Commons Attribution 4.0 International License.
