Solving the convection-diffusion problem in the horizontal cylindrical annulus by the R-function method and its application for thermal accelerometer simulation

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.