A. V. Rukavishnikov

Institute of Applied Mathematics FEB RAS (Khabarovsk, Russian Federation)

Abstract. In the paper a system of non-stationary incompressible Navier-Stokes equations in skew-symmetric form with inhomogeneous Dirichlet boundary conditions is considered. The domain is a bounded non-convex polygon with an incoming corner at the boundary. The problem is described in skew-symmetric form, rather than in the well-known convective form, due to the fact that an approximate solution of the latter one often disrupts the kinetic energy balance in turbulent flows. By discretizing the initial system of equations in time and linearizing it, an Oseen-type problem is obtained at each time layer. A concept of an $R_{\nu}$-generalized solution in sets of S.L. Sobolev weighted spaces is defined. A scheme of weighted finite element method is constructed based on this concept. A definition of an approximate $R_{\nu}$-generalized solution is introduced. A comparative numerical analysis of the errors in solutions in skew-symmetric and convective forms is conducted, as well as in the weighted and classical finite element methods of the problem under consideration. In both comparisons, the advantage of the approach proposed is demonstrated.

Key Words: Navier-Stokes equations, skew-symmetric form, weighted FEM, incoming angle

For citation: A. V. Rukavishnikov. Numerical analysis of the Navier-Stokes equations in skew-symmetric form in a domain with an incoming corner. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:2(2026), 62–82. DOI: https://doi.org/10.15507/2079-6900.28.202602.62-82

Information about the author:

Alexey V. Rukavishnikov, Ph.D. (Phys. and Math.), Leading Researcher, Institute of Applied Mathematics (Russian Academy of Science, Far Eastern Branch) (60 Serysheva Str., Khabarovsk, 680038, Russia), ORCID: http://orcid.org/0000-0002-7585- 4559, 78321a@mail.ru