src/test/collapse.c

    Rayleigh collapse of a compressible gas bubble

    A gas bubble at lower pressure collapses in a viscous fluid in the absence of surface tension forces.

    The fluids are either viscous or inviscid and we compare the evolution of the radius with the Rayleigh-Plesset and Keller-Miksis models.

    See also section 4.2.4 of Fuster & Popinet, 2018.

    Results for an inviscid fluid

    set xlabel 't/tR'
set ylabel 'R/R_0'
set key bottom
pg0 = 100.
pinf = 5.*pg0
tR = 0.915*sqrt(1./(pinf - pg0))
plot "../collapse-inviscid/log" u ($1/tR):($2*3.)**(1./3.) every 4 w p pt 6 t "Basilisk", \
     "RPinviscid.dat" u ($1/tR):2 w l lw 2 t 'Rayleigh-Plesset',			    \
     "" u ($1/tR):3 w l lw 2 t 'Keller-Miksis'
    Bubble radius as a function of time (script)

    Bubble radius as a function of time (script)

    For adiabatic gas transformations P_b V_b^{\gamma} should remain constant inside the bubble.

    set ylabel 'p V^{/Symbol g}'
plot "../collapse-inviscid/log" u ($1/tR):(($2*3.)**(1.4)*$4) not w l
    Entropy errors (script)

    Entropy errors (script)

    The bubble does not remain spherical.

    set xlabel 'x'
set ylabel 'y'
set size ratio -1
plot "../collapse-inviscid/out" u 1:2 not w l
    Interfaces (script)

    Interfaces (script)

    Results for a viscous fluid

    reset
set xlabel 't/tR'
set ylabel 'R/R_0'
set key bottom
plot "log" u ($1/tR):($2*3.)**(1./3.) every 3 w p pt 6 t "Basilisk", \
     "../collapse-spherical/log" u ($1/tR):($2*3.)**(1./3.) every 3 w p pt 8 t "Basilisk (1D)", \
     "RP.dat" u ($1/tR):2 w l lw 2 t 'Rayleigh-Plesset',             \
     "" u ($1/tR):3 w l lw 2 t 'Keller-Miksis',                      \
     "RPinviscid.dat" u ($1/tR):3 w l lw 2 t "Keller-Miksis (inviscid)"
    Bubble radius as a function of time (script)

    Bubble radius as a function of time (script)

    For adiabatic gas transformations P_b V_b^{\gamma} should remain constant inside the bubble.

    set ylabel 'p V^{/Symbol g}'
plot "log" u ($1/tR):(($2*3.)**(1.4)*$4) not w l
    Entropy errors (script)

    Entropy errors (script)

    The bubble remains more spherical than in the inviscid case.

    set xlabel 'x'
set ylabel 'y'
set size ratio -1
plot "out" u 1:2 not w l
    Interfaces (script)

    Interfaces (script)

    References

    [brennen2014]

    Christopher E Brennen. Cavitation and bubble dynamics. Cambridge university press, 2014.
    [keller1980]

    Joseph B Keller and Michael Miksis. Bubble oscillations of large amplitude. The Journal of the Acoustical Society of America, 68(2):628–633, 1980.

    We run both the (1D) spherically-symmetric and the (2D) axisymmetric versions.

    #if SPHERICAL
# include "spherisym.h"
#else
# include "axi.h"
#endif
#include "bubble.h"

int main()
{
  pinf = 5.*pg0;
  tend = 2.50001*0.915*sqrt (1./(pinf - pg0)); // fixme: stops too early with 2.5

#if INVISCID
  MAXLEVEL = 12;
#else // !INVISCID
  MAXLEVEL = 11;
  double Reynolds = 10.;
  mu1 = sqrt(pinf - pg0)/Reynolds;

    Rayleigh-Plesset like models neglect the gas viscosity. Here we put a small value.

      mu2 = mu1*0.0001;
#endif // !INVISCID
  
  CFLac = 10.;
  gamma2 = 1.4;
  gamma1 = 7.14;
  PI1 = 300*pg0;
     
  L0 = 50;
#if TREE  
  N = 1 << MINLEVEL;
#else
  N = 1 << MAXLEVEL;
#endif
  run();
}