Fictitious domain approach for numerical modelling of Navier–Stokes equations

Abstract

This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so-called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second-order accuracy in time and space. A multigrid local mesh refinement is also implemented, using 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 step, some iterations of the augmented Lagrangian method combined with a preconditioned 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 behind a backward-facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright © 2000 John Wiley & Sons, Ltd.