A novel meshless method for mathematical simulation of the convection-diffusion problem in the thermal accelerometers with different cylindrical annulus geometry is proposed. The technique is based on the R-Function method (RFM) that, by means of the analytical description of an arbitrary boundary, allows one to construct the so-called solution structure that satisfies the given boundary conditions exactly. This solution structure is represented in the form of the series with unknown coefficients and it can be used as a functional expansion in some variational methods (the least squares, the Galerkin, et al.). It is shown that the RFM gives the possibility to represent an approximate solution with appropriate accuracy, taking a relatively small number of the expansion terms. Such simple semi-analytical solutions to the diffusion-convection problems are used for identification of the main thermal characteristics of thermal accelerometers. The ways for improving the device performance are analyzed.
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24 November 2020
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019
23–28 September 2019
Rhodes, Greece
Research Article|
November 24 2020
Solving the convection-diffusion problem in the horizontal cylindrical annulus by the R-function method and its application for thermal accelerometer simulation
Mikhail Basarab;
Mikhail Basarab
a)
1
Bauman Moscow State Technical University (BMSTU)
, Bldg. 5, 2nd Baumanskaya Str., 105005, Moscow, Russia
a)Corresponding author: bmic@mail.ru
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Alain Giani;
2
IES, Université Montpellier 2
, Batiment 5, 860 Rue Saint Priest, 34095, Montpelier, France
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Philippe Combette;
Philippe Combette
2
IES, Université Montpellier 2
, Batiment 5, 860 Rue Saint Priest, 34095, Montpelier, France
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Igor Ivanov
Igor Ivanov
1
Bauman Moscow State Technical University (BMSTU)
, Bldg. 5, 2nd Baumanskaya Str., 105005, Moscow, Russia
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a)Corresponding author: bmic@mail.ru
AIP Conf. Proc. 2293, 030031 (2020)
Citation
Mikhail Basarab, Alain Giani, Philippe Combette, Igor Ivanov; Solving the convection-diffusion problem in the horizontal cylindrical annulus by the R-function method and its application for thermal accelerometer simulation. AIP Conf. Proc. 24 November 2020; 2293 (1): 030031. https://doi.org/10.1063/5.0026612
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