Numerical simulations of thermally stratified flows in an open domain

Thierry Dubois (1) , Rachid Touzani (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We present two dimensional numerical simulations of circulation induced by a heat island in an unbounded domain. The °ow is thermally stratified in the vertical direction. Boussinesq equations in a closed domain are used to describe the flow variables. For this problem, very elongated computational domains have to be used in order to obtain accurate solutions. A term, whose effect is to smoothly damp the convective terms in a layer close to the vertical boundaries, is introduced in the temperature equation. Therefore, shorter domains can be considered. This method is investigated through the numerical simulations of stationary solutions at Rayleigh number $Ra = 10^5$ and $2.5x10^5$. Time periodic solutions at $Ra = 5x10^5$ and $10^6$ are also reported and analyzed.

Mots clés: Boussinesq equations; incompressible flows; natural convection; finite difference scheme; open domain; heat island circulation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]

Thierry Dubois, Rachid Touzani. Numerical simulations of thermally stratified flows in an open domain. European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006, 2006, Delft, Netherlands. ⟨hal-00109088⟩