Ilia Marchevsky
Publications:
Kotsur O. S., Shcheglov G. A., Marchevsky I. K.
Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments
2022, Vol. 18, no. 3, pp. 423439
Abstract
This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible
fluid, for which approximate weak solutions are sought in the class of vortex filaments.
In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by
the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time,
for viscous incompressible flows described by the system of Navier – Stokes equations, the search
for such generalized solutions in the finite time interval is generally difficult. In this paper, we
propose a method for transforming the diffusion term in the vorticity evolution equation that
makes it possible to construct its approximate solution in the class of vortex filaments under
the assumption that there is no helicity of vorticity. Such an approach is useful in constructing
vortex methods of computational hydrodynamics to model viscous incompressible flows.
