Energy equation
 

Hi
I'm trying to solve the energy equation for the cavity problem. the flow is incompressible and natural convection is neglected. only terms that are considered in the equation are convection and diffusion terms. the boundary condition on horizontal walls are temperature constant and isolation on vertical walls. the problem is that the temperature inside the domain near the hot wall exceeds the boundary value. It would be great if someone could help me and give me any suggestion.

thanks

Maybe you are using non-monotone schemes ...otherwise check for numerical oscillations due to the instability

I'm using first order upwind scheme. i was wondering to know if we put aside accuracy,is there going to be a physically correct result? would you please be kind and tip me with some other schemes?

in your case there is no coupling of the temperature with the velocity field, thus it is only a passive scalar. The values in the interior (in absence of production terms) must be bounded by the BC.s Dirichlet value. Therefor check the stability constraint of your scheme. How do you discretize the diffusion term? For an FTUS/FTCS method the stability constraint requires a small time step for low cell Reynolds number...

The problem is steady state. I discretized the equation as it is written in chapter 5 of versteeg. the problem gives the same answer for finite volume and element based finite volume method. if i change the boundary condition so that vertical walls have constant temperature and horizontal walls be isolated the values in the interior doesn't exceed boundary value.