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3D Incompressible Turbulent Flow in a Parallelipipedic Cavity

Binous M. S., Abide S., Zeghmati B., Hedi H.

Machine Dynamics Research

2016

Vol. 40, No. 2

5--18

This work investigates the turbulent flow in a ventilated cavity by means of numerical simulations. In particular, simulations are performed using a parallel compact fourth-order spatial discretization and the sub-grid scale (SGS) model Wall Adapting Local Eddy (WALE). Results focuses on the turbulence statistics and are validated against experimental data, for which a good agreement is observed. So, this contribution illustrates how compact schemes can be used to combine high-order accuracy with complex flow.

Method of lines for the incompressible Navier-Stokes equations in the stream-function formulation

Kosma Z.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2005

Vol. 9, No 1

17-35

The aim of this paper is to simulate the laminar motion of viscous incompressible fluid and the transition between the laminar and the turbulent state in simply connected domains. The developed numerical algorithms are based on the solution of an initial-boundary value problem for the full incompressible Navier-Stokes equations, written in the form of a fourth-order equation for the stream function. The spatial derivatives and the boundary conditions are discretized on uniform grids by means of sixth-order compact schemes together with fourth-order finite-difference formulas, while the continuity of the time variable is preserved. The resulting system of ordinary differential equations has been integrated using the backward-differentiation predictor-corrector method. The efficiency of the numerical algorithms is demonstrated by solving two problems of viscous liquid plane flows in a square driven cavity and a backward-facing step. Calculations for the cavity flow configuration have been obtained for Reynolds numbers ranging from Re=100 to Re=30000 on uniform 50×50 and 100×100 grids. Calculations for the backward-facing step have been made for Re ≤ 3000 with channel lengths, L, within the range 10-30, on 30L×30 uniform grids. The computed stream-function contours and velocity fields have been compared with numerical results reported in the literature.