High accuracy solutions of incompressible Navier-Stokes equations
TLDR
In this article, high accuracy finite difference approximations were developed for partial differential equations of elliptic type, with particular emphasis on the convection-diffusion equation, and they were extended to the solution of Navier-Stokes equations.Citations
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Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers
TL;DR: Numerical calculations of the 2-D steady incompressible driven cavity flow are presented and comparisons are made with benchmark solutions found in the literature.
Journal ArticleDOI
Solving PDEs with radial basis functions
Bengt Fornberg,Natasha Flyer +1 more
TL;DR: During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems.
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A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations
Ming Li,Tao Tang,Bengt Fornberg +2 more
TL;DR: In this article, the Navier-Stokes equations were approximated to fourth-order accuracy with stencils extending only over a 3 x 3 square of points, and the key advantage of the new compact 4-order scheme is that it allows direct iteration for low-to-mediwn Reynolds numbers.
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Viscous linear stability analysis of rectangular duct and cavity flows
TL;DR: In this paper, the viscous linear stability of four classes of incompressible flows inside rectangular containers is studied numerically and the partial-derivative eigenvalue problem which governs the temporal development of global three-dimensional small-amplitude disturbances is solved numerically.
References
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High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
U Ghia,K.N Ghia,C. T. Shin +2 more
TL;DR: The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions.
Journal ArticleDOI
Driven cavity flows by efficient numerical techniques
TL;DR: In this paper, an efficient and reliable numerical technique of high-order accuracy is presented for solving problems of steady viscous incompressible flow in the plane, and is used to obtain accurate solutions for the driven cavity.
Journal ArticleDOI
A single cell high order scheme for the convection-diffusion equation with variable coefficients
TL;DR: In this paper, a schema de differences finies for convection-diffusion coefficients variables is proposed, and the resulting system is resolué par des methodes iterative.
Journal ArticleDOI
An adaptive multigrid technique for the incompressible Navier-Stokes equations
TL;DR: An automatic adaptive refinement technique has been coupled to the multigrid approach to produce an efficient and stable solution strategy for solving the steady-state incompressible Navier-Stokes equations.
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