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13.2  PASS: Relaxation of a charge bump

Author
Jose M. López-Herrera Sánchez
Command
sh bump.sh
Version
100610
Required files
bump.gfs (view) (download)
bump.sh norms.ref
Running time
36 seconds

A concentrated bump of charge of the form,

ρe(x,t=0)=
exp
x2+y2
2a2
a 
2 π

is initially set in a single fluid of conductivity K and permittivity ε. Due to conduction the bump decays exponentially in time (see figure 121) as

ρe(x,t)=ρe(x,t=0) exp(−K t/ε) 

while preserving the initial geometry (see figure 122).


Figure 121: Temporal decay of the charge density at (0,0). (Continuous) analytical solution, (symbols) Gerris EHD module.


Figure 122: Spatial distribution of charge density along the radial axis (times equal 0, 2, 4 and 6 are shown). (continuous) analytical solution, (symbols) present simulation.


Figure 123: Evolution of the norms of the error on the charge density distribution shown in figure 122.


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