Proceedings of the 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020)

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A Numerical Algorithm of Determining the Coefficients and Functions of Sources in the Filtration Equation

Authors
Sergey Shergin
Corresponding Author
Sergey Shergin
Available Online 10 November 2020.
DOI
10.2991/aisr.k.201029.013How to use a DOI?
Keywords
inverse problem, pseudoparabolic equation, filtration, fissured rock, numerical solution
Abstract

The inverse problems of recovering the right-hand side and coefficients in a pseudoparabolic equations of filtration with the use of the pointwise overdetermination are studied. We expose some existence and uniqueness theorems which are the base of a numerical algorithm of recovering the right-hand side (the source function), left-hand side (coefficient problem) and a solution. The problem is well-posed and the stability estimates hold. It can be reduced to a Volterra-type integral equation, where the operator has a small norm for small time segments. The finite element method is used to reduce the problem to a system of ordinary differential equations which is solved by the finite difference method. The idea of the predictor-corrector method is employed in the algorithm. The results of numerical experiments are presented. They show a good convergence of an approximate solutions to a solution. Also this article can develop models and algorithms for modeling situations in a decision support system. For problems arising in determining the parameters of the reservoir where oil is produced or determining the flow rates of wells.

Copyright
© 2020, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020)
Series
Advances in Intelligent Systems Research
Publication Date
10 November 2020
ISBN
978-94-6239-265-6
ISSN
1951-6851
DOI
10.2991/aisr.k.201029.013How to use a DOI?
Copyright
© 2020, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - CONF
AU  - Sergey Shergin
PY  - 2020
DA  - 2020/11/10
TI  - A Numerical Algorithm of Determining the Coefficients and Functions of Sources in the Filtration Equation
BT  - Proceedings of the 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020)
PB  - Atlantis Press
SP  - 62
EP  - 67
SN  - 1951-6851
UR  - https://doi.org/10.2991/aisr.k.201029.013
DO  - 10.2991/aisr.k.201029.013
ID  - Shergin2020
ER  -