Notes and figures for the discussion about chemotaxis with Chris Budd

Index:

alpha and R ] - [ double vs quad ] - [ Umax(delta) ] - [ Umax(cte) ]



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alpha and R

Near the core u looks like u0*(1+u0*x^2) with u0=1/R^2 and R=K(Tc-t)^(0.5+alpha) with alpha(t)=1/sqrt(-2*log(Tc-t)).
Here we plot alpha(t) and R(t) (for Tc=0.5):
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double vs quad

Comparison between quad (green) and double (pink) precision runs.
ubar (approx inside the core) in red
psi (approx outside of the core) in blue
The largest curves (resp. double and quad) corresponds to highest possible u0 obtained numerically.

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Umax vs monitor exponent

Behaviour of the maximum height umax for different exponents delta used in the monitor function:

      M=1+|u|^{0.5+delta}

The numerics stopped when:

oscillations: when umax(t) reached a maximum and then started oscillating
crash: when the numerics crashed (stiffness/min step reached)


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Umax vs monitor constant

Behaviour of the maximum height umax for different constants cte used in the monitor function:

      M=cte+|u|^{0.5}

The numerics stopped when:

oscillations: when umax(t) reached a maximum and then started oscillating
crash: when the numerics crashed (stiffness/min step reached)


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