[CIG-CS] Discontinuous viscosity
Wolfgang Bangerth
bangerth at math.tamu.edu
Sun Mar 11 22:27:40 PDT 2012
> One interesting detail is that it is necessary to change the
> fundamental variables, because I do not have expressions for the jumps
> in velocity. To that end, I use the augmented velocity, which is the
> ordinary velocity multiplied by the viscosity.
That may be in analogy to the mixed Laplace formulation: when you have
- div k(x) grad p = f
then the mixed formulation is
k^{-1} u + grad p = 0
- div u = 0
and not
u + k grad p = 0
- div u = 0
The former leads to a reasonable error bound whereas the latter leads to
a system where the error grows proportional to
max k(x) / min k(x)
The same would be true when rewriting things as
u + grad p = 0
- div k u = f
Best
W.
------------------------------------------------------------------------
Wolfgang Bangerth email: bangerth at math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/
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