scholarly journals Comparative analysis of numerical methods for determining parameters of chemical reactions from experimental data

2021 ◽  
Vol 2092 (1) ◽  
pp. 012011
Author(s):  
Aleksei Prikhodko ◽  
Maxim Shishlenin ◽  
Olga Stadnichenko
Keyword(s):  
Inverse Problem ◽  
Chemical Reactions ◽  
Gradient Methods ◽  
Correlation Method ◽  
Optimization Methods ◽  
Adjoint Problem ◽  
Problem Solution ◽  
Implicit Methods ◽  
Identifiability Analysis ◽  
Reaction Rate Constants

Abstract The aim of this paper is to select an optimal numerical method for determining the parameters of chemical reactions. The importance of the topic is due to the modern needs of industry, such as the improvement of chemical reactors and oil or gas processing. The paper deals with the problem of determining reaction rate constants using gradient methods and stochastic optimization algorithms. To solve an forward problem, implicit methods for solving stiff ODE systems are used. A correlation method of practical identifiability of the required parameters is used. The genetic algorithm, particle swarm method, and fast annealing method are implemented to solve an inverse problem. The gradient method for the solution of the inverse problem is implemented, and a formula for gradient of the functional is given with the corresponding adjoint problem. We apply an identifiability analysis of the unknown coefficients and arrange the coefficients in the order of their identifiability. We show that the best approach is to apply global optimization methods to find the interval of global solution and after that we refine inverse problem solution using gradient approach.

Analysis of Different Kinds of Measurements on the Estimation of Time Dependent Mass and Heat Transfer Coefficients in Drying

2004 ◽  
Author(s):  
Leonardo F. Saker ◽  
Helcio R. B. Orlande ◽  
Cheng-Hung Huang ◽  
Gligor H. Kanevce ◽  
Ljubica P. Kanevce
Keyword(s):  
Inverse Problem ◽  
Adjoint Problem ◽  
Time Dependent ◽  
Problem Solution ◽  
Function Estimation ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Dependent Mass ◽  
Estimation Of Time ◽  
Local Moisture

In this paper we present the solution of the inverse problem of simultaneously estimating the heat and mass transfer coefficients at the surface of a drying one-dimensional body. The physical problem is formulated in terms of the linear Luikov equations and the unknown functions are time dependent. The inverse problem is solved by using the conjugate gradient method of function estimation with adjoint problem. Results are presented for the estimation of discontinuous functions by using simulated measurements of local temperature, local moisture content and/or total moisture weight. The main objective of the paper is to examine the effects of different types of measurements on the inverse problem solution.

scholarly journals On the modeling of ultrasound wave propagation in the frame of inverse problem solution

2021 ◽  
Vol 2099 (1) ◽  
pp. 012044
Author(s):  
N S Novikov ◽  
D V Klyuchinskiy ◽  
M A Shishlenin ◽  
S I Kabanikhin
Keyword(s):  
Inverse Problem ◽  
Gradient Descent ◽  
Finite Volume Methods ◽  
Adjoint Problem ◽  
Order System ◽  
Ultrasound Wave ◽  
Problem Solution ◽  
Coefficient Inverse Problem ◽  
Acoustic Sounding ◽  
First Order

Abstract In this paper we consider the inverse problem of detecting the inclusions inside the human tissue by using the acoustic sounding wave. The problem is considered in the form of coefficient inverse problem for first-order system of PDE and we use the gradient descent approach to recover the coefficients of that system. The important part of the sceme is the solution of the direct and adjoint problem on each iteration of the descent. We consider two finite-volume methods of solving the direct problem and study their Influence on the performance of recovering the coefficients.

scholarly journals Macroscopic Entropy of Non-Equilibrium Systems and Postulates of Extended Thermodynamics: Application to Transport Phenomena and Chemical Reactions in Nanoparticles

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 802 ◽  
Author(s):  
Sergey Serdyukov
Keyword(s):  
Chemical Reactions ◽  
Constitutive Equations ◽  
Linear Equations ◽  
Reaction Diffusion ◽  
Irreversible Thermodynamics ◽  
Entropy Density ◽  
Higher Order ◽  
Reaction Diffusion Systems ◽  
Reaction Rate Constants ◽  
Thermodynamic Variables

In this work, we consider extended irreversible thermodynamics in assuming that the entropy density is a function of both common thermodynamic variables and their higher-order time derivatives. An expression for entropy production, and the linear phenomenological equations describing diffusion and chemical reactions, are found in the context of this approach. Solutions of the sets of linear equations with respect to fluxes and their higher-order time derivatives allow the coefficients of diffusion and reaction rate constants to be established as functions of size of the nanosystems in which these reactions occur. The Maxwell-Cattaneo and Jeffreys constitutive equations, as well as the higher-order constitutive equations, which describe the processes in reaction-diffusion systems, are obtained.

scholarly journals The inverse coefficient problem of heat transfer in layered nanostructures

2017 ◽  
Vol 20 (3) ◽  
pp. 213-219
Author(s):  
K. K. Abgarian ◽  
R. G. Noskov ◽  
D. L. Reviznikov
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Thermal Resistance ◽  
Transfer Problem ◽  
Dominant Role ◽  
Rapid Development ◽  
Problem Solution ◽  
Microwave Range ◽  
Contact Thermal Resistance ◽  
Resistance Coefficients

The rapid development of electronics leads to the creation and use of electronic components of small dimensions, including nanoelements of complex, layered structure. The search for effective methods for cooling electronic systems dictates the need for the development of methods for the numerical analysis of heat transfer in nanostructures. A characteristic feature of energy transfer in such systems is the dominant role of contact thermal resistance at interlayer interfaces. Since the contact resistance depends on a number of factors associated with the technology of heterostructures manufacturing, it is of great importance to determine the corresponding coefficients from the results of temperature measurements.The purpose of this paper is to evaluate the possibility of reconstructing the thermal resistance coefficients at the interfaces between layers by solving the inverse problem of heat transfer.The complex of algorithms includes two major blocks — a block for solving the direct heat transfer problem in a layered nanostructure and an optimization block for solving the inverse problem. The direct problem was formulated in an algebraic (finite difference) form under the assumption of a constant temperature within each layer, which is due to the small thickness of the layers. The inverse problem was solved in the extreme formulation, the optimization was carried out using zero-order methods that do not require the calculation of the derivatives of the optimized function. As a basic optimization algorithm, the Nelder—Mead method was used in combination with random restarts to search for a global minimum.The results of the identification of the contact thermal resistance coefficients obtained in the framework of a quasi-real experiment are presented. The accuracy of the identification problem solution is estimated as a function of the number of layers in the heterostructure and the «measurements» error.The obtained results are planned to be used in the new technique of multiscale modeling of thermal regimes of the electronic component base of the microwave range, when identifying the coefficients of thermal conductivity of heterostructure.

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