Fictitious domain approach for numerical modelling of Navier-Stokes equations

This study investigates a fictitious domain model for the numerical solutio n of various incompressible viscous flows. It is based on the so-called Nav ier-Stokes/Brinkman and energy equations with discontinuous coefficients al l over an auxiliary embedding domain. The solid obstacles or walls are take n into account by a penalty technique. Some volumic control terms are direc tly introduced in the governing equations in order to prescribe immersed bo undary conditions. The implicit numerical scheme, which uses an upwind fini te volume method on staggered Cartesian grids, is of second-order accuracy in time and space. A multigrid local mesh refinement is also implemented, u sing the multi-level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time st ep, some iterations of the augmented Lagrangian method combined with a prec onditioned Krylov algorithm allow the divergence-free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behi nd a backward-facing step. The numerical results are shown in good agreemen t with other published numerical or experimental data. Copyright (C) 2000 J ohn Wiley & Sons, Ltd.