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Hi Nektar-users,

I am doing stability analysis on the 2D Rayleigh Benard Posillue (RBP) Flow. I am using the Boussinesq approximation as the buoyancy force. I get the correct eigenvalue for the direct mode. However, when I change the EvolutionOperator to Adjoint, I cannot get the correct eigenvalue.

Here are some details, since the Adjoint LNS equation is different from Direct LNS (Adj LNS and Dir LNS equation are attached in the figure for your convenience). The body force for the Direct LNS in v-mom is const*c1 (c1 is the scalar). But in Adjoint LNS, there is a new term (const*v) in the scalar equation. So the body forces need to be modified as,

<FUNCTION NAME="BodyForce">
            <E VAR="u" VALUE="0" />
            <E VAR="v" VALUE="0" />
            <E VAR="c1" VALUE="const*v" EVARS="v" /> 
</FUNCTION>

I am wondering if I can put it into the scalar equation (c1) as the above function. Or any idea is welcome.  

Thank you for your time
Yours
Yicheng