[mcfdma]

Hello.

I need some guidance with writing equations in my header file.

I am working on electrohydrodynamic (EHD) solver that uses interFoam+electrostatics elements (http://openfoamwiki.net/index.php/Co...ectromagnetics)

As you can see from the above link, the third equation that is the charge conservation equation is written as (the two equations are the same where 1st one is used in the link above and the other one is the same but written using different variables).
Screenshot 2021-02-17 174400.png

In my header file, I have written

        tmp<fvScalarMatrix> ECDEqn
        (
            fvm::ddt(rhoE) 
          - fvc::laplacian(sgm, Ue)
          + fvm::div(phi, rhoE)
        );

        solve(ECDEqn);

However, I have read an article [1] that simplifies this equation into:Screenshot 2021-02-17 173711.png
where K is equivalent to the previous equation's sigma.

I have tried rewriting my header file equation but only this seems to be working. Is it correct?

        tmp<fvScalarMatrix> ECDEqn
        (
          fvm::laplacian(sgm, Ue)

        );

        solve(ECDEqn);

I tried many ways including solve(ECDEqn == 0) but was unsuccessful.

Can someone guide me on how to write the simplified equation?

Many thanks


[1] https://iopscience.iop.org/article/1...17/23/1/015004