[Kellis]

Hello all,

I am attempting to solve a conjugate heat transfer problem where viscous heating plays an important role in the overall process. I am solving the energy equation as follows:



Due to the nature of the problem, the viscous heating term varies many orders of magnitude over the width of a few cells, and causes some instabilities / oscillations when solving for the temperature. To combat this, I am hoping to implement some sort of smoothing algorithm which conserves the overall amount of viscous heating, but distributes it within a wider area to make the computation more stable. For instance in 1D, assuming a uniform grid spacing, this smoothing algorithm might turn a field that looks like this:

[ 1 1 1 10 1 1 1 ]

Into one which looks like this:

[ 1 2 3 4 3 2 1 ]

Ideally, the "width" of the spread would be controllable by the user. I am sure such an algorithm exists already, but I am not sure what the correct search terms would be, and my initial efforts to find such a method have not yielded any good leads.

If anyone has a suggestion for a method I might try, I would be grateful. Additionally, any other strategies I might try to increase the stability of the problem would be appreciated.

Thanks,
Kellis