I am solving a energy transport equation of the form

drhoH/dt + del.(rho V H) = -dP/dt+...+.

in a collocated arrangement. I see that as the simulation progresses, the sources due to dp/dt is highly unstable.

How can I stabilize my computation? The computation is for an incompressible flow but with heat transfer.

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CFDtoy

What kind of time-marching scheme do you use?.For multi-stage R-K it might be unclear how to discretize dp/dt on RHS.

I am using a simple backward euler (implicit for stability!) Does any time splitting work?

CFDtoy

The stability analysis is based on linearized theories and hence you cannot necessarily guarantee stability for non linear problems.Did you check if explicit time marching worked for this particular case?

explicit time stepping posed a lot of problems..since i hd problems in converging them.

normally when the source terms are not functions of the flw variables and cause such kind of stability problem..is there a way to reduce their propagation !>!? I am not aware of time splitting schmes for these purposes?

anythin related?

Thanks for your cmments harish.

-- CFDtoy

I have never come across anything either.Is there any reason for using the equation for enthalpy instead of total energy or internal energy.Those equations do not have a time dependent pressure term and your implicit euler implementation might be easier.

In case of total enthalpy, you do require the dp/dt term on the RHS. Also, finding temp using total enthalpy seemed easier.

CFDtoy

I think it would be the same even if you use the equation for internal energy.