A multilevel method applied to the numerical simulation of two-dimensional incompressible flows past obstacles at high Reynolds number.

François Bouchon (1) , Thierry Dubois (1) , Nicolas James (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this paper we present an extension of the spectral multilevel method developed by F. Bouchon and T. Dubois to the case of numerical simulation of two-dimensional flows past obstacles. These mutlilevel methods have first been adapted to the context of the finite difference discretization of the Navier-Stokes equations on staggered Cartesian grids. Here, this approach is coupled with an immersed boundary method, which allows to handle complex geometries Numerical results are presented and compared to direct simulations where no multilevel strategy is used. At Reynolds number 9500, comparisons are shown between the multilevel method on a 512^2 mesh and a direct simulation on a 3072^2 mesh. At Reynolds number 500 000, the multilevel method is robust, while the corresponding direct simulation (same grid, same time-step) blows up in the first time-iterations of the solution.

Mots clés: Incompressible flows; Multilevel scheme; Cut cell; Immersed boundary

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

François Bouchon, Thierry Dubois, Nicolas James. A multilevel method applied to the numerical simulation of two-dimensional incompressible flows past obstacles at high Reynolds number.. 2010. ⟨hal-00570093⟩