In MFIX Equations 2012-1 (January 2012), I found that energy equations are written in non-conservation form while species transport equations are written in conservation form, which is shown below:
In my knowledge, they are supposed to be both written in conservation form since they are both derived based on control volume.
I also found some clues in PNNL mfix presentation, in which a reference for energy equation is given. However, this reference can’t be downloaded anymore. I would appreciate if you could help me with this question or can offer this reference!
Generally, the conservation of the total internal energy equation (enthalpy equation is widely used) should be solved. The temperature equation is mathematically equivalent to the total internal energy equation,while cannot be recast on a conservative form without reverting to enthalpy or internal energy equation.
Even though conservation and non-conservation forms are not numerically equivalent when implemented using a numerical method. Solving the temperature equation is more robust and without reducing the numerical accuracy, while solving the enthalpy equation sometimes is likely affected by numerical oscillations.
