visc.C

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visc.C

This code solves the dffusion equation.

We consider as a model problem teh paraboic equation with variable coefficient v to demonstrate the treatment of the viscous contributions:

$u_t=\nabla \cdot (\nu \nabla u)+f, \mbox{in}\hspace{2mm} \Omega, u \in L^2(\Omega)$

$u=g(x,t), \mbox{on}\hspace{2mm} \partial \Omega$

We then introduce the flux variable

and re-write the parabolic equation,after integrating by parts twice, we obtain an equivalent formulation which is easier to implement. The new variational problem is:

$(u_t,w)_{E_i}=(-\nabla \cdot q,w)_{E_i}-<w,(q^B-q^I) \cdot n >_{E_i} + (f,w)_{E_i}, \forall w \in L^2(\Omega)$

$\frac {1}{\nu}(q,v)=(-\nabla u,v)_{E_i}-<(u^B-u^I)n,v>_{\partial E_i}, \forall v \in H(grad;\Omega)$

u=g(x,t), on $\partial \Omega$

Comp_Deriv
Diff_Step_NS
Average_edges
calc_vis
Calc_Ncons_edges
Set_Dir_BCs
Save_Conv
Restore_Conv

Guang Lin
2001-03-08