Inverse Problem of Pipeline Transport of Weakly-Compressible Fluids

Gamzaev, Kh. M.

doi:10.1007/s10891-020-02261-x

“…where δ-the error level, ξ(t) is a random variable, modeled using a random number sensor. In this case, the value of the regularization parameter is determined by the residual principle [1], [3]. Numerical experiments were carried out on a space-time difference grid with steps of ∆t = 0.5 s, ∆x = 0, 02 m for the following exact values of the desired function ψ e (t) = 0.4; 0.6; 0.85 m 3 /kg at d = 0.5 m 2 /s, k = 0, 5…”

Section: Results Of Numerical Calculationsmentioning

confidence: 99%

“…The correctness of the formulation of boundary inverse problems and their solutions' existence and uniqueness in various functional classes are investigated in [6], [10], [11], [13], [14]. Numerical methods for solving boundary inverse problems for parabolic equations are considered in many papers [1], [3], [4], [15], [17].…”

Section: Problem Statementmentioning

confidence: 99%

Numerical solution of one inverse problem for a diffusion model of a chemical-technological process

BAYRAMOVA,

Hamzayev

2023

BMJ

0

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A chemical-technological process taking place in a chemical reactor with a chemical reaction of the second order is considered. A one-dimensional one-parameter diffusion model of the hydrodynamic flow in the reactor is proposed for the mathematical description of this process. Within the framework of the proposed model, the inverse problem is posed to determine the concentration of the selected reagent in the incoming flow, ensuring the implementation of a predetermined hydrodynamic regime at the reactor outlet. A discrete analogue of the inverse problem is constructed and the resulting difference problem is presented as a variational problem with local regularization. A special representation is proposed for the numerical solution of the variational problem. As a result, an explicit formula is obtained for determining the approximate concentration of the selected reagent in the incoming stream. The effectiveness of the proposed method is illustrated by numerical calculations for model problems

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“…where δ-the error level, ξ(t) is a random variable, modeled using a random number sensor. In this case, the value of the regularization parameter is determined by the residual principle [1], [3]. Numerical experiments were carried out on a space-time difference grid with steps of ∆t = 0.5 s, ∆x = 0, 02 m for the following exact values of the desired function ψ e (t) = 0.4; 0.6; 0.85 m 3 /kg at d = 0.5 m 2 /s, k = 0, 5…”

Section: Results Of Numerical Calculationsmentioning

confidence: 99%

“…The correctness of the formulation of boundary inverse problems and their solutions' existence and uniqueness in various functional classes are investigated in [6], [10], [11], [13], [14]. Numerical methods for solving boundary inverse problems for parabolic equations are considered in many papers [1], [3], [4], [15], [17].…”

Section: Problem Statementmentioning

confidence: 99%

Untitled

2023

BMJ

0

View full text Add to dashboard Cite

A chemical-technological process taking place in a chemical reactor with a chemical reaction of the second order is considered. A one-dimensional one-parameter diffusion model of the hydrodynamic flow in the reactor is proposed for the mathematical description of this process. Within the framework of the proposed model, the inverse problem is posed to determine the concentration of the selected reagent in the incoming flow, ensuring the implementation of a predetermined hydrodynamic regime at the reactor outlet. A discrete analogue of the inverse problem is constructed and the resulting difference problem is presented as a variational problem with local regularization. A special representation is proposed for the numerical solution of the variational problem. As a result, an explicit formula is obtained for determining the approximate concentration of the selected reagent in the incoming stream. The effectiveness of the proposed method is illustrated by numerical calculations for model problems

show abstract