Hi Dumux developers,
I have just done some simulations of the advection-diffusion equation
(Figure_1, simplified from 1p2c model in Dumux) on three 2D-in-3D grids.
Case (A), the first grid resides on the XOY plane, the mesh (B) and (C) are
obtained by rotating the mesh (A) around Y-axis by an angle \alpha with
cos (\alpha) =1/sqrt(5)) and 90°, repectively. Consequently, the mesh (C)
resides on the YOZ (see the Figure_2, A: white, B: blue, C: yellow).
*/ Initial condition: P=P0, c = 0.
*/ Boundary conditions:
- Y = Ymin: P=2P0, c=C0,
- Y = Ymax: P=P0, c=0 (It means that the flow is along Y-axis)
- No-flux Neumann condition for the remaining boundaries.
Viscosity is constant, gravity is neglected. The diffusion effect is very
smaller than the convection one (V*L/D ~1E7). Since gravity is neglected,
in principle, the result of these three simulations should be the same: the
front of the concentration profile travels with a velocity V. But,
curiously, this is not the case. The travelling velocity of front of the
concentration curve in the case (A) is equal to \sqrt(5) time in the case
(B). Furthermore, in the case (C), there was a convergence problem: Linear
solver did not converge.
It seems that the permeability in the case (B) Kyy(B) equal to 1/sqrt(5) of
the one in the case (A), Kyy(A), and Kyy(C) = 0. I think that it may be a
bug (?) in the transformation from global to normal vector cooridnate of
the reference element in the box method on 2D-in-3D mesh when using
FoamGrid. Could you please check it and confirm me?
I'm sorry for this long email and I hope I was clear with that.
Kind regards,
Tri Dat
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