Changes between Version 14 and Version 15 of u/BonnorEbertMatched2
 Timestamp:
 10/15/12 21:39:59 (12 years ago)
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u/BonnorEbertMatched2
v14 v15 48 48 '''B&P, classic outsidein collapse''' 49 49 50 'Classic B&P collapse' of a BE sphere. That is, 10% density enhancement of sphere above equilibrium values, in pressure equilibrium with a light (rho=0.01rho(Rbe) ) ambient. This, as well as the following plots, show lineouts through the center of the sphere of the quantities: rho, absolute value(radial velocity), absolute value(mach), and pressure, all normalized to their initial values in the grid. The xaxis is logarithmic and begins at the length of the smallest zone dx. The yaxis is linear: http://www.pas.rochester.edu/~erica/BPJuly22.gif . The collapse here resembles the B&P results, namely collapse proceeds in an outsidein fashion and remains subsonic most of the way through. 51 50 52 [[Image(BPrho.png, 20%)]] 51 53 [[Image(B&P_vrad.png, 20%)]] … … 55 57 '''Stability''' 56 58 59 Stability test of the critical BE sphere placed in an ambient rho=0.01rho(Rbe), with sphere and ambient in pressure equilibrium at r=Rbe. This is just the B&P sphere, with no density enhancement, in a box twice as large. My apologies, but the movie is broken into 2, with the first half here: https://clover.pas.rochester.edu/trac/astrobear/attachment/wiki/u/BonnorEbertMatched/rhoCroppedLight.gif and second half here: https://clover.pas.rochester.edu/trac/astrobear/attachment/wiki/u/BEmoviesLonger/rhoSecondHalf.gif. This setup was stable to collapse for at least 5 crossing times, where 1 tc= 0.2 in computational units, as can be seen from this 2d slice through the center of the sphere. Here the sphere is breathing about its equilibrium initial condition. 60 57 61 [[Image(rhoLight.png, 20%)]] 58 62 [[Image(vradLight.png, 20%)]] … … 60 64 61 65 '''Matched''' 66 67 BE sphere in an ambient rho= rho(Rbe). This is the same setup as above, except now there is no 10% rho enhancement and the ambient has same density as BE sphere at r=Rbe. http://www.pas.rochester.edu/~erica/MatchedJuly26.gif Here collapse seems to be proceeding in a very different manner. At small times, material begins to pile up at the sphere's outer edge. After enough material has accumulated, the pressure at the sphere's outer edge exceeds critical values and moves inward with time in a compression wave. The collapse is supersonic most of the way through. Note, radial velocity is now the actual quantity, to show clearly the sign (<0 is moving inward, >0 is moving outward). 68 62 69 [[Image(rhoMatched.png, 20%)]] 63 70 [[Image(VradMatched.png, 20%)]] 64 71 [[Image(MatchedJuly26.gif, 20%)]] 65 66 72 67 73 … … 84 90 I ran a series of simulations to study the deviation from the 'classic' collapse studies of the BE sphere  a slight increase in density values above equilibrium of a critical sphere (xi=6.5) in pressure equilibrium with its environment (Foster and Chevalier, 1993, Banerjee and Pudritz, 2003). My simulations were all variations of the B&P setup, but with a sphere in a domain twice the size (~30 Rbe), and varying ambient densities. These runs are as follows: 85 91 86 1) Stability test of the critical BE sphere placed in an ambient rho=0.01rho(Rbe), with sphere and ambient in pressure equilibrium at r=Rbe. This is just the B&P sphere, with no density enhancement, in a box twice as large. My apologies, but the movie is broken into 2, with the first half here: https://clover.pas.rochester.edu/trac/astrobear/attachment/wiki/u/BonnorEbertMatched/rhoCroppedLight.gif and second half here: https://clover.pas.rochester.edu/trac/astrobear/attachment/wiki/u/BEmoviesLonger/rhoSecondHalf.gif. This setup was stable to collapse for at least 5 crossing times, where 1 tc= 0.2 in computational units, as can be seen from this 2d slice through the center of the sphere. Here the sphere is breathing about its equilibrium initial condition. 92 87 93 88 94 2) 'Classic B&P collapse' of a BE sphere. That is, 10% density enhancement of sphere above equilibrium values, in pressure equilibrium with a light (rho=0.01rho(Rbe) ) ambient. This, as well as the following plots, show lineouts through the center of the sphere of the quantities: rho, absolute value(radial velocity), absolute value(mach), and pressure, all normalized to their initial values in the grid. The xaxis is logarithmic and begins at the length of the smallest zone dx. The yaxis is linear: http://www.pas.rochester.edu/~erica/BPJuly22.gif . The collapse here resembles the B&P results, namely collapse proceeds in an outsidein fashion and remains subsonic most of the way through. 89 95 90 3) BE sphere in an ambient rho= rho(Rbe). This is the same setup as above, except now there is no 10% rho enhancement and the ambient has same density as BE sphere at r=Rbe. http://www.pas.rochester.edu/~erica/MatchedJuly26.gif Here collapse seems to be proceeding in a very different manner. At small times, material begins to pile up at the sphere's outer edge. After enough material has accumulated, the pressure at the sphere's outer edge exceeds critical values and moves inward with time in a compression wave. The collapse is supersonic most of the way through. Note, radial velocity is now the actual quantity, to show clearly the sign (<0 is moving inward, >0 is moving outward).91 96 92 4) 3 simulations at equally spaced ambient densities between the light and matched cases: 93 http://www.pas.rochester.edu/~erica/Light105July22.gif 94 http://www.pas.rochester.edu/~erica/Light70July22.gif 95 http://www.pas.rochester.edu/~erica/Light35July22.gif 97 96 98 97 99