METHOD AND STUDY OF THE ACCURACY OF CALCULATING THE MATHEMATICAL MODEL OF THE ELECTROHYDRAULIC EFFECT

Abstract

The mathematical model of the electrohydraulic effect (EHE) is a nonlinear non-stationary system of partial differential equations (PDE), which reflects the motion and contact interaction of two media, gaseous and liquid, under the action of pulsed thermal excitation. Such PDE systems generally do not have analytical solutions and are solved only by numerical methods, which are approximate in nature, i.e. they provide a solution with some error. The peculiarity of the motion of media in the case of EHE is large deformations in the form of flows and vortices. This feature imposes significant restrictions on the choice of the method for solving the PDE model. The widely known Lagrangian finite element method used to solve contact problems, in the case of EHE modeling leads to a pathological change in the shape of the finite elements, and therefore to instability of the calculation process and an unlimited increase in error. In calculation practice, a variant of the finite element method, FEM-ALE, has become widespread. It uses both Lagrangian and Eulerian grids of nodes and a special advection procedure, i.e., transfer by interpolation of the solution from the Lagrangian grid to the Eulerian one, and then vice versa from the Eulerian one to another new Lagrangian grid. Such an additional interpolation procedure, which is used repeatedly in the calculation, leads to additional (in comparison with the Lagrangian FEM) errors. If the causes and kinetics, as well as the methods of error control in the case of the Lagrangian FEM, have been sufficiently studied in the literature, then the kinetics of error development in the simulation of the EGE using the FEM-ALE method has been practically not studied. The article is devoted to the study of the development of errors in the numerical solution in this particular case. An analytical solution of the problem in the asymptotic case for a technological system with a rigid chamber is obtained. This solution is analyzed in comparison with the numerical solution using the FEM-ALE method. Conclusions are made regarding the errors in calculating pressure as the main factor of mechanical impact of EGE on the technological object and technological equipment, as well as errors in calculating deformations of gaseous and liquid media.

The scientific novelty consists in the development of a method for determining the accuracy of EHE parameter calculations using the MSE-ALE method. The practical value lies in determining the accuracy of calculating the parameters of the EHE mathematical model, which makes it possible to justify the use of numerical modeling as a method of researching technological processes and systems using EHE