The computation is on a 2D heated back-facing step flow. The temperature of the bottom and top walls is imposed to $T_c$ and the temperature of the step walls is $T_h$. The inflow is fixed with an uniform velocity profile $U_b$ at temperature $Tc$. We consider an incompressible flow under the Boussinesq hypothesis : the physical properties are constant and the thermal buoyancy effect is modelised by the Boussinesq hypothesis : $F_b= -\rho_0.\beta.g_0.(T - T_0)$ (see the page Gravity for more details). We suppose the fluid is air that behaves as a perfect gas. As a consequence, $\beta= \frac{1}{T_0}$

The governing equations for incompressible flows are shown here.

Reference scales for the dimensionless problem :

• the fluid density $\rho_0$
• the bulk velocity $U_b$
• the kinematic viscosity $\mu_0$
• the step height
• the temperature $T_c$

From the previous reference scales, we define the Reynolds number : $Re_h= \frac{\rho_0 \dot U_b \dot h}{\mu_0}$ and the dimensionless temperature $T*= \frac{T}{T_c}$.
We therefore deduce the following dimensionless data :

• Fluid density $\rho_0*=1$
• Inflow bulk velocity $U_b*= 1$
• Bottom and top wall temperature $T_c*=1$
• Thermal expansion coefficient $\beta*=1$
• Step height $h*= 1$

Any other data of the problem are set to :

• Domain length : $L*=12$
• Domain height : $H*= 2$
• Step length : $l*= 2$
• Reynolds number $Re_h= 100$
• Step wall temperature $T_h*= 2$
• Gravity constant $g*= \frac{g_0 \dot h}{U_b^2}= 1$
• Prandtl number $Pr= 0.71$

We now build the data file by selecting the relevant namelists in the lookup list. We only keep the relevant variables (that must be explicitly set). The others ones are removed. We need to set :

• Data set on the fluid properties
• Data set on the computational domain
• Data set on physical quantity initialization over the domain
• Data set on forces on the fluid
• Data set on the boundary conditions
• Data set on the numerical methods
• Data set on the simulation control
• Data set on the output data