[physicosm]

Dear OpenFoamers,Foamers and HopeFoamers,


I am struggling lately with the problem of how to solve a non linear 4rth order diffusion equation(see below). Of course, it can be solved full explicitly but on this way someone has to use small time-steps. One idea is to split this equation into two 2nd order equations by defining the brackets as the chemical potential. When someone does this, it will come up with the problem of OpenFOAM and general most of the softwares/toolkits can't solve equations for two variables simultaneously. With OpenFOAM words: FATAL ERROR incompatible fields. Nevertheless, I have attached a picture that I was thinking on this way maybe I could solve my problem but it doesn't work. The idea was to calculate first explicit the chemical potential in order to find the correct values of C and then, to calculate implicity the chemical potential with the new correct values of C that have been calculated in the previous step. After this, you solve the diffusion equation. This idea doesn't work. Therefore, I would like to ask if someone has any idea of how to deal with this problem. Last, of course the ideal case would be to define an implicity laplacian^2 with an implicit scheme but I guess this over my programming skills. Thanks in advance!


Thomas