Towards understanding the algorithms for solving the Navier–Stokes equations

SV Ershkov, EY Prosviryakov… - Fluid Dynamics …, 2021 - iopscience.iop.org
In this paper, we present a review of featured works in the field of hydrodynamics with the
main aim to clarify the ways of understanding the algorithms for solving the Navier–Stokes …

[HTML][HTML] Solving the hydrodynamical system of equations of inhomogeneous fluid flows with thermal diffusion: A review

SV Ershkov, EY Prosviryakov, NV Burmasheva… - Symmetry, 2023 - mdpi.com
The present review analyzes classes of exact solutions for the convection and thermal
diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck …

[HTML][HTML] Exact solutions to the Navier–Stokes equations with couple stresses

ES Baranovskii, NV Burmasheva, EY Prosviryakov - Symmetry, 2021 - mdpi.com
This article discusses the possibility of using the Lin–Sidorov–Aristov class of exact solutions
and its modifications to describe the flows of a fluid with microstructure (with couple …

Exact solutions to the Navier–Stokes equations describing stratified fluid flows

NV Burmasheva, EY Prosviryakov - … технического университета. Серия …, 2021 - mathnet.ru
The paper considers the necessity of constructing exact solutions to the equations of
dynamics of a viscous fluid stratified in terms of several physical characteristics, with density …

[HTML][HTML] Exact Solutions of Navier–Stokes Equations for Quasi-Two-Dimensional Flows with Rayleigh Friction

N Burmasheva, S Ershkov, E Prosviryakov… - Fluids, 2023 - mdpi.com
To solve the problems of geophysical hydrodynamics, it is necessary to integrally take into
account the unevenness of the bottom and the free boundary for a large-scale flow of a …

Exact Solutions for Isobaric Inhomogeneous Couette Flows of a‎ Vertically Swirling Fluid

S Ershkov, E Prosviryakov… - Journal of Applied and …, 2023 - jacm.scu.ac.ir
The paper generalizes the partial class of exact solutions to the Navier–Stokes equations.
The proposed exact solution describes an inhomogeneous three-dimensional shear flow in …

Точное решение уравнений Навье-Стокса, описывающее пространственно неоднородные течения вращающейся жидкости

НВ Бурмашева, ЕЮ Просвиряков - Труды Института математики и …, 2020 - mathnet.ru
При исследовании точного решения было уставлено, что разрешимость системы
уравнений возможна при алгебраической связи горизонтальных градиентов …

A new class of exact solutions of the Oberbeck–Boussinesq equations describing an incompressible fluid

VV Privalova, EY Prosviryakov - Theoretical Foundations of Chemical …, 2022 - Springer
A new class of exact solutions of the Oberbeck–Boussinesq equations for incompressible
media is constructed taking into account body forces, heat sources (sinks), and Joule …

Exact solutions for steady convective layered flows with a spatial acceleration

NV Burmasheva, EY Prosviryakov - Russian Mathematics, 2021 - Springer
In this paper, we study non-one-dimensional convective layered flows of a viscous
incompressible fluid with a spatial acceleration. We perform the simulation on the base of …

Inhomogeneous gradient Poiseuille flows of a vertically swirled fluid

N Burmasheva, S Ershkov, E Prosviryakov… - Journal of Applied and …, 2024 - jacm.scu.ac.ir
An exact solution is proposed for describing the steady-state and unsteady gradient
Poiseuille shear flow of a viscous incompressible fluid in a horizontal infinite layer. This …