Comparative analysis of the accuracy of OPENFOAM solvers for the oblique shock wave problem

Abstract

The use of modern polymeric materials as dielectrics makes it possible to increase operational characteristics of the elements of various electric power and electronic devices. The necessary combination of interconnected values of permissible electric field strength and maximum operating temperature is crucial when choosing a particular polymer material. The relationship of these parameters is nonlinear due to the nonlinear dependence the electrical resistivity and the thermal conductivity coefficient on temperature of the polymer material. This relationship can be represented in a closed analytical form of integral relations in which the variable limit of the integrals is the desired function describing the temperature distribution in the dielectric layer. A quantitative analysis of these ratios for five different polymeric materials with known electrothermal characteristics has been carried out. The results of calculations of the temperature state of the dielectric layer and the distribution in the layer of the absolute value of the electric field intensity are given. The presented results can be used to justify the choice of a particular polymer material as a dielectric in the designed devices.

Generalized Computational Experiment and Visual Analysis of Multidimensional Data

“…In a practical sense, this makes it possible to reveal hidden dependences of valuable functionals on the determining parameters of the problem, similar to the above formulas. This work continues a series of works devoted to the development and implementation of a generalized computational experiment for various classes of computational aerodynamics problems [3][4][5][6][7][8][9][10][11][12][13][14]. Despite the fact that there are very few works devoted to the development of a generalized computational experiment, the development of such experiments is gradually taking place in many areas.…”

“…Also, such a formal formulation allows numerical study of optimization analysis problems, when the inverse problem is solved at each point of the grid partition of the multidimensional space of the determining parameters. Both types of similar problems are considered in a series of papers [3][4][5][6][7][8][9][10][11][12][13][14]. The only way to effectively carry out a generalized numerical experiment is applying of parallel computations.…”

“…The revealed dependencies can be further approximated by geometric primitives in order to obtain a generalizing dependence, which will represent the solution of interest for a class of problems. Examples of the implementation of this approach are presented in [5][6][7][8][9][10][11][12][13][14]. Also, to reduce the dimension of a multidimensional array, methods of mapping into embedded manifolds of smaller dimension are very effective [27][28][29].…”

“…The results obtained made it possible to get a general idea of the calculation errors for all solvers. [14]. As a result, an oblique shock wave is formed before the start of the plate.…”

“…4. The distribution of pressure in the vicinity of the shock wave for different solvers in comparison with exact solution [14].…”