A New Approach to the Use of Non-Primitive Variables in the Mechanics of Continuous Media

Abstract

The problem of an approximate solution to hydrodynamic problems is the consideration of pressure. To exclude it from the equations, the transition to “non-primitive variables” (vortex and velocity vector divergence) is made. In this case, there are difficulties in the algorithmization of new equations for solving the inverse problem of hydrodynamics and a lot of internal iterative calculations. The object of this study includes equations in “non-primitive” variables. The research methods are based on the transformation without simplifications and assumptions of hydrodynamic equations into a form containing “non-primitive” variables and the demonstration of the possibilities of solving the equations. The GAMS programming language was used for approximate solutions for the first time. The aim of this paper is to demonstrate the possibility of solving the full equations in “non-primitive” variables for various conditions. The results showed the possibility of considering the compressibility of the medium when solving the inverse problem of hydrodynamics; the identity of solutions of the proposed system of equations and equations using the potential; and the possibility of using optimizing programming languages for hydrodynamics problems. The scientific novelty of this research consists of solving the full equations of hydrodynamics with the use of “non-primitive” variables but without the use of the current function. Doi: 10.28991/ESJ-2024-08-02-021 Full Text: PDF

Keywords

• continuous medium
• non-primitive variable
• vortex
• motion vector potential
• compressibility of the medium.