Conclusion

This article provides a succinct presentation of the physical phenomena involved in fluid mechanics, and in particular their modeling by the Navier-Stokes equations in laminar flow. The resolution of the latter equation is particularly complex, and only the finite difference method has been considered as a discretization method to date. This latter technique is compatible, on the one hand, with the current-vorticity formulation on classical finite-difference meshes and, on the other hand, with the velocity-pressure formulation on finite-difference meshes, preferably shifted to minimize the effect of instabilities. Concerning time discretization, the numerical stability of time schemes has been studied in the two-dimensional case (and one-dimensional in appendix 3 (§