An efficient scheme for solving steady incompressible Navier-Stokes equations.

*(English)*Zbl 0699.76034Summary: The steady incompressible Navier-Stokes equations in a 2D driven cavity are solved in primitive variables by means of the multigrid method. The pressure and the components of the velocity are discretized on staggered grids, a block-implicit relaxation technique is used to achieve a good convergence and a simplified FMG-FAS algorithm is proposed. Special focus on the finite differences scheme used to approach the convection terms is made and a large discussion with other schemes is given. Results in a square driven cavity are obtained for Reynolds numbers as high as 15,000 on fine uniform meshes and the solution is in good agreement with other studies. For \(Re=5000\) the secondary vortices are very well represented showing the robustness of the method. For Reynolds numbers higher than 5000 the loss of stability for the steady solution is discussed. Moreover, some computations on a rectangular cavity of aspect ratio equal to two are presented. In addition the method is very efficient as far as CPU time is concerned; for instance, the solution for \(Re=1000\) on a 128\(\times 128\) grid is obtained within 24 s on a SIEMENS VP 200.

##### MSC:

76D05 | Navier-Stokes equations for incompressible viscous fluids |

76M99 | Basic methods in fluid mechanics |

##### Keywords:

steady incompressible Navier-Stokes equations; driven cavity; multigrid method; block-implicit relaxation technique; simplified FMG-FAS algorithm; SIEMENS VP 200
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\textit{C.-H. Bruneau} and \textit{C. Jouron}, J. Comput. Phys. 89, No. 2, 389--413 (1990; Zbl 0699.76034)

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