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Function File: [A] = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta)

Build the Scharfetter-Gummel stabilized stiffness matrix for a diffusion-advection problem in cylindrical coordinates with axisymmetric configuration. Rotational symmetry is assumed with respect to be the vertical axis r=0. Only plane geometries that DO NOT intersect the symmetry axis are admitted. 

    |   ____                 _|____ 
    |  |    \               \ |    |
  z |  |     \  OK           \|    |   NO!
    |  |______\               |\___|
    |     r                   |

The equation taken into account is:

1/r * d(r * Fr)/dr + dFz/dz = f

with

F = [Fr, Fz]’ = - alpha * gamma ( eta grad (u) - beta u )

where alpha is an element-wise constant scalar function, eta and gamma are piecewise linear conforming scalar functions, beta is an element-wise constant vector function.

Instead of passing the vector field beta directly, one can pass a piecewise linear conforming scalar function phi as the last input. In such case beta = grad phi is assumed.

If phi is a single scalar value beta is assumed to be 0 in the whole domain.

See also: bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction, bim2a_advection_diffusion, bim2c_mesh_properties.

Package: bim