Ensuring the accuracy and stability of computer simulation of electronic devices is an important problem in their design. The greatest difficulties in simulation of electronic devices arise in the case of the analysis of self-oscillating circuits, since mathematical models of such circuits can be stiff and oscillating at the same time. The aim of this work is to develop an efficient numerical method for solving ordinary differential equations that provides higher accuracy of time domain analysis for various types of autogenerators compared to existing methods. The proposed method is a hybrid method and is based on the well-known Gear and trapezoidal methods used in simulators of electronic circuits. To evaluate the accuracy of the proposed method and known methods a generalized model of a self-oscillating circuit was used for which an analytical solution was determined in the steady-state operating mode. The accuracy of the numerical solution was determined based on the analysis of errors in estimating the main parameters of the oscillatory process – the amplitude and frequency of oscillations. A comparative analysis of errors in estimating the amplitude and frequency of oscillations in autogenerators demonstrates the high efficiency of the proposed hybrid method for analyzing both harmonic oscillators and relaxation oscillators. A further increase in the accuracy of the hybrid method is possible using implicit Runge-Kutta methods (Rado IIA and Lobatto IIIA subclasses), which have L- and P-stability, respectively. It should be noted that with an increase in the order of accuracy of implicit Runge-Kutta methods, the computational complexity of these methods increases, but for the Rado IIA and Lobatto IIIA subclasses the increase in computational complexity will be minimal.
А.А. Medeltsev, P. А. Shapovalov, М. V. Voronov, А. I. Polukhina, P.N. Sigaleva, А.V. Frolov
2022-04-21
Abstract ▼
The article presents a numerical simulation of non-stationary convective-conductive heat transfer of the strapdown inertial navigation system (SINS), developed in the JSC «CNIIAG». The numerical simulation is carried out in the ANSYS Mechanical. The aim of the study is a comprehensive analysis of heat exchange processes, which are characteristic to the device operation, including mutual spatial influence of thermal powers on each other, as well as on the block of sensitive elements. The simulation of heat transfer inside the hermetic case of the SINS is carried out for critical operating conditions in a strongly and weakly coupled consideration with a comparison of both approaches. ANSYS Mechanical, CFX and System Coupling simulation modules are chosen for program implementation of each approach. The k-e model of air turbulence with implicit consideration of the effect in the boundary layers and diffusion correction in shear flows is chosen for this approach. External heat exchange with ambient air is considered by setting convective boundary conditions on the external surfaces of the SINS, considering their orientation. To obtain numerical values of the heat transfer coefficients, the orientation of each surface in space is taken into account by using the appropriate coefficient. The presence of irregularities on the surfaces of the SINS in the contacts between solid components is considered by using the calculation of thermal resistances of the actual contact and intercontact layer. The simulation results of deformed state of SINS structural system, resulting from the action of a non-symmetric thermal field, is presented. The analysis of the obtained graphs is carried out. Stiffness indicators of the SINS structural system is defined as angles of deviation of sensitivity axes caused by thermal deformations. The obtained results make it possible to evaluate the engineering solutions for the quality of heat removal from the elements of the PCBs, bypassing the sensitive elements of the device, adopted at the stage of product layout.
