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<p>The paper derives equations to describe mass transfer in a porous medium on a graph with additional constraints for the mass flow rate on some edges, which can serve as a model of an irrigation system with valves on some pipes. The problem of mass transfer in a porous medium on a graph with additional constraints for the flow rate on the edges is formulated and modeled. The existence of a solution to this problem is justified for the case of an unsaturated medium as the initial condition and monotonically increasing boundary conditions. A numerical method for approximating the solution to the formulated problem is constructed based on the numerical methods for solving one-dimensional mass transfer problems with regard for constraints on the flow rate. The results of computational experiments are presented.</p>

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Mass Transfer Problem with Saturation Limit and Flow Constraints in a Porous Graph-Structured System

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • D. A. Klyushin,
  • V. A. Kolesnykov,
  • S. I. Lyashko

摘要

The paper derives equations to describe mass transfer in a porous medium on a graph with additional constraints for the mass flow rate on some edges, which can serve as a model of an irrigation system with valves on some pipes. The problem of mass transfer in a porous medium on a graph with additional constraints for the flow rate on the edges is formulated and modeled. The existence of a solution to this problem is justified for the case of an unsaturated medium as the initial condition and monotonically increasing boundary conditions. A numerical method for approximating the solution to the formulated problem is constructed based on the numerical methods for solving one-dimensional mass transfer problems with regard for constraints on the flow rate. The results of computational experiments are presented.