The method of boundary integral equations in the boundary value problems of dynamics of fluids and gases

Abstract

Based on the created generalized apparatus of vector-tensor analysis, integral representations of the main dynamic and kinematic characteristics of the problem of viscous gas flow around force systems of arbitrary spatial shape are constructed. The boundary value problem of the interaction of such systems with a viscous gas flow is reduced to a system of linear, conditioned by physical boundary conditions, boundary integral equations regarding the kinematic and dynamic characteristics of the problem. It is proven that all the obtained characteristics depend on the newly obtained irrotational vector potential of the momentum, which significantly simplifies the integral representations of solutions and their numerical implementation. On the basis of the created generalized apparatus of vector-tensor analysis, integral representations of the main dynamic and kinematic characteristics of the problem of the flow of a viscous gas flow around supporting systems of satisfactory spatial form have been constructed. The boundary value problem of the interaction of such systems with a viscous gas flow is reduced to a system of linear, conditioned by physical boundary conditions, boundary integral equations regarding the kinematic and dynamic characteristics of the problem. It is proven that all the obtained characteristics depend on the newly obtained, vortex-free vector potential of the momentum, which significantly simplifies the integral representations of the solutions and their numerical implementation.

Full Paper