False convection in Thermal fluid flow

Mo Yun

Dear numerical expert,

I have a false numerical thermal problem.

There is a duct (2D) with length of long (20 times of height of the duct) with heated on top and bottom wall and with a inlet with cold fluid inflow (for example. temperature is zero and hot walls are 1.0).

When I applied a upwind difference scheme to the energy equation, the temperature in the duct seems reasonable but its accuracy is low as we know that at last it has first order acuracy.

To get a high order accuracy answers, I used the central diffence scheme in discretizing the convection terms. I got a converged answer but the temperature near the inlet showed minus solutions. Of course, it is not correct but it has the second accuracy answer!

By testing the blending factor between the upwind and the central diffence, the reasonable soltions rest in the upwind side. I have no available imagination to check if there are such a kind of solutions for the velocity component but it could be done for the energy transportation.

I think this kind of problem is not new but it really needs to solve. Central-Upwind hybrid sheme, Exponential scheme, QUICK, LOAD, CONDIF schemes exist but which one is the best, with high order spatial accuracy and with stable characteristics?

Is it correct by setting some limiters in the solving the eneergy eqs. but the central difference scheme is still adopted. To avoid the divergence, the upwind scheme is applied to the coefficient and the source terms due to the central diffence are modified.

I am expecting any advices.

Yun Mo