Discussion Forum

Hello all,
I'm Francesco Vergottini, phd student at the university of Palermo.
I'm a bit confused about the implementation of the diffusion equation in the Transport of Diluted Species Module and the way Comsol treats the Material and the Spatial Frame.This is what I've understood: the diffusion equation written in the Material Frame is :

D(C)/Dt=-grad dot(Diffusivity_matrix (dot) grad(C)), where:

"dot" is the scalar product
"D(C)/Dt" s the material derivative,
"Diffusivity_matrix" is the 2*2 matrix of the diffusion coefficient in 2D.

When I define the equation in the Material Frame and look at the Weak Expressions Tab in the Equation View Node, I read:
-root.mod1.cTIME*test(c)-(chds.DXX_c*cX+chds.DXY_c*cY)*test(cX)-(chds.DYX_c*cX+chds.DYY_c*cY)*test(cY)
which is the correct weak formulation of the problem, because root.mod1.cTIME should represent the material derivative, D(C)/Dt. So, in my opinion, this formulation should account for the convective transport, which is incorporated in the
D(C)/Dt term. The convective transport arises from the material deformation, which is calculated through the Structural Mechanics Module
When I define the equation in the Spatial Frame and look at the weak expressions in the Equation View Node, I read:
-(root.mod1.cTIME-cx*d(x,TIME)-cy*d(y,TIME))*test(c)-(chds.Dxx_c*cx+chds.Dxy_c*cy)*test(cx)-(chds.Dyx_c*cx+chds.Dyy_c*cy)*test(cy)
in this expression the term root.mod1.cTIME-cx*d(x,TIME)-cy*d(y,TIME) should represent the partial derivative of C with respect to time, in fact d(x,TIME) and d(y,TIME) should be the x and y component of the velocity vector (if I've correctly understood) and cx, cy are the partial derivatives of C with respect to x and y. This expression should not account for the convective transport and, in fact, when I run the simulations, the two different formulation gives me different results.
I've also tried to run a simulation defining the diffusion equation in the Spatial Frame and adding the convective term. The velocity field is that calculated by the Sructural Mechanics Module . I expected that ,in this way, I' would have got the same results obtained with the first case (material frame without convection), but I did not.
Anyone can help me?
Regards,
Francesco Vergottini