Numerical solution of BVP for the incompressible Navier–Stokes equations at large Reynolds numbers
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Dmitri V. Lomasov
Abstract
The problems of numerical modelling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier–Stokes equations exist at large Reynolds numbers, but they are unstable and lead to transient or turbulent unsteady regimes. In addition, the solution of the boundary value problem at large values of Reynolds number may be non-unique. In this paper, we consider numerical algorithms for finding such stationary solutions. We use natural pressure-velocity variables under standard finite element approximation on triangular grids. Iterative methods with different linearizations of convective transport are used to test a two-dimensional problem of incompressible fluid flow in a square-section cavity with a movable top lid. The developed computational algorithm allowed us to obtain two solutions when the Reynolds number exceeds a critical value for flows in a cavity of semi-elliptical cross-section.
Funding statement: This work has been supported by the Russian Science Foundation (grant 23-41-00037).
Acknowledgment
We sincerely thank the anonymous reviewer for their careful review and constructive comments, which have greatly improved the manuscript.
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Articles in the same Issue
- Frontmatter
- A two-level parallelization algorithm for the direct simulation Monte Carlo method of problems of rarefied gas dynamics
- Conservative correction of the sequential noniterative scheme for reactive transport problems with minerals precipitation–dissolution and variable media properties
- Numerical solution of BVP for the incompressible Navier–Stokes equations at large Reynolds numbers
- Low-rank Monte Carlo method for aggregation kinetics with particle sources
- Numerical simulation of propeller aerodynamics and tonal noise using parallel code ‘Gerbera’
