Abstract
As well as many modern devices, thermal accelerometers (TAs) need a sophisticated mathematical simulation to find the ways for their performance optimization. In the paper, a novel approach for solving computational fluid dynamics (CFD) problems in the TA’s cavity is proposed (MQ-RFM), which is based on the combined use of Rvachev’s R-functions method (RFM) and the Galerkin technique with multiquadric (MQ) radial basis functions (RBFs). The semi-analytical RFM takes an intermediate position between traditional analytical approaches and numerical methods, such as the finite-element method (FEM), belonging to the family of the so-called meshless techniques which became popular in the last decades in solving various CFD problems in complex-shaped cavities. Mathematical simulation of TA by using the MQ-RFM was carried out with the purpose to simulate the temperature response of the device and to study and improve its performance. The results of numerical experiments were compared with well-known analytical and numerical benchmark solutions for the circular annulus geometry and it demonstrated the effectiveness of the MQ-RFM for solving the convective heat-transfer problem in the TA’s cavity. The use of solution structures allows one to take a relatively small number of expansion terms to achieve an appropriate accuracy of the approximate solution satisfying at the same time the given boundary conditions exactly. The application of the MQ-RFM gives the possibility to obtain semi-analytical solutions to the diffusion-convection problems and to identify the main thermal characteristics of the TA, that allows one to improve the device performance.
Highlights
Many modern devices, in particular, sensors based on microelectromechanical systems (MEMS), need a sophisticated mathematical simulation to find the ways of their optimization
The semi-analytical solution was obtained in a closed form of the MQ-radial basis functions (RBFs) and it satisfied the boundary conditions exactly
The technique was applied to the well-studied benchmark problem of convection in the circular annulus, which is the simplest model of the thermal accelerometer
Summary
In particular, sensors based on microelectromechanical systems (MEMS), need a sophisticated mathematical simulation to find the ways of their optimization. When applying the RFM, if a domain consists of two parts, for example, “inner” and “outer”, which characteristic dimensions are not comparable, one needs to take either a large higher power of approximating polynomials (in spectral methods) that worsens computational stability, or a very small regular or irregular mesh width for bases of compactly supported functions. In the latter case, the RFM loses its main benefits and can be practically considered as a conventional grid method such as FDM or FEM.
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