13.2 PASS:
Relaxation of a charge bump

Author
 Jose M. LópezHerrera 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,
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
ρ_{e}(x,t)=ρ_{e}(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. 