Algorithm for solving the Navier–Stokes equations for the modeling of creeping flows

We study a coupled algorithm for solving the two-dimensional Navier–Stokes equations in the stream function–vorticity variables. The algorithm is based on a finite-difference scheme in which the inertial terms in the vortex transport equation are taken from the lower time layer and the dissipative t...

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Bibliographic Details
Published in:Differential equations 2017-07, Vol.53 (7), p.949-963
Main Authors: Kamyshin, V. E., Mazhorova, O. S.
Format: Article
Language:English
Subjects:
Algorithms
Computational fluid dynamics
Difference and Functional Equations
Differential equations
Dissipation
Finite difference method
Fluid flow
Mathematical models
Mathematics
Mathematics and Statistics
Modelling
Navier-Stokes equations
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Stokes law (fluid mechanics)
Velocity
Vorticity
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Summary:We study a coupled algorithm for solving the two-dimensional Navier–Stokes equations in the stream function–vorticity variables. The algorithm is based on a finite-difference scheme in which the inertial terms in the vortex transport equation are taken from the lower time layer and the dissipative terms, from the upper time layer. In the linear approximation, we study the stability of this algorithm and use test computations to show its advantages when modeling flows at moderate Reynolds numbers.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266117070114