A second-order immersed boundary method for the numerical simulation of two-dimensional incompressible viscous flows past obstacles.

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

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We present a new cut-cell method, based on the MAC scheme on Cartesian grids, for the numerical simulation of two-dimensional incompressible f lows past obstacles. The discretization of the nonlinear terms, written in conservative form, is formulated in the context of finite volume methods. While first order approximations are used in cut-cells the scheme is globally second-order accurate. The linear systems are solved by a direct method based on the capacitance matrix method. Accuracy and efficiency of the method are supported by numerical simulations of 2D flows past a cylinder at Reynolds numbers up to 9 500.

Mots clés: Immersed boundary method; Cartesian grid method; Cut-cell method; Incompressible viscous flows; Complex geometry

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

François Bouchon, Thierry Dubois, Nicolas James. A second-order immersed boundary method for the numerical simulation of two-dimensional incompressible viscous flows past obstacles.. 2010. ⟨hal-00570090⟩