ISSN 2079-6900 (Print)
ISSN 2587-7496 (Online)

#### Middle Volga Mathematical Society Journal

MSC2020 35Q35, 35Q74, 65M06

### Mathematical modeling of pressure measurement systems in gas-liquid media

#### P. A. Velmisov1, Yu. A. Tamarova2

Annotation The article discusses the initial-boundary value problems for systems of differential equations, which are mathematical models of the mechanical system "pipeline - pressure sensor that is designed to measure pressure in gas-liquid media. On the basis of the proposed models, the joint dynamics of the pressure sensor sensitive element and of the working medium in the pipeline connecting the sensor to the combustion chamber of the engine is investigated. To describe the movement of the working medium, linear models of the mechanics of liquid and gas are used; to describe the dynamics of the sensitive element, both linear and nonlinear models of the mechanics of a solid deformable body are used. The solutions of stated initial-boundary value problems are carried out on the basis of the Galerkin method and the finite-difference method. differential equations, aeroelasticity, pipeline, pressure sensor, elastic element, dynamics, finite difference method, Galerkin method

1Velmisov Petr Aleksandrovich, Head of the Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), Professor, Dr.Sci. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-7825-7015, velmisov@ulstu.ru

2Tamarova Yuliya Aleksandrovna, Postgraduate Student, Department of Higher Mathematics, Ulyanovsk State Technical University (32 Severny Venets St., Ulyanovsk 432027, Russia), ORCID: http://orcid.org/0000-0001-6408-1573, kazakovaua@mail.ru

Citation: P. A. Velmisov, Yu. A. Tamarova, "[Mathematical modeling of pressure measurement systems in gas-liquid media]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:3 (2020) 352–367 (In Russian)

DOI 10.15507/2079-6900.22.202003.352-367