Variable Viscosity (Numerical Stability)
I'm solving some two phase flow problems and have started working on varying the viscosity ratio. I am using a a Crank Nicholson method for the viscous terms. I noticed that for a viscosity ratio of say 0.1 the method become unstable for too large of a time step. If I switch to a backward Euler method the solution behaves nicely for the same time step.
From what I remember the Crank Nicholson method is A-Stable which had something to do with producing decaying oscillations. Does anyone have any references about the Crank Nicholson method becoming unstable for problem with jumps or shocks or discontinuities in coefficients. I know Stefan Turek has done some work with the Fractional-Step theta scheme. Anyone have experience with that?
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