Changes between Version 23 and Version 24 of u/erica/JeansTest

Timestamp:

07/25/13 10:29:39 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/JeansTest

@@ -149 +149 @@
 Thus we should see the characteristic growth rate of [[latex($\omega$)]]. 
 
+For further info, you can download the Mathematica calculations [http://www.pas.rochester.edu/~erica/AstroCalcs.nb here]
+
+and the code
+[http://www.pas.rochester.edu/~erica/JeansInstabProblem.f90 here]
 
 = Results = 
@@ -154 +158 @@
 Analytic function - 
 
-Since I am having difficulty saving an initial density function in astrobear for use with !ProblemBeforeStep, I just plotted the analytical function for the initial density perturbation and the perturbation after an e-folding time in Mathematica. The e-folding time in physical units is ~6 Myr, and in computational units corresponds to t = 0.0016.  
+Here is the plotted analytical function for the initial density perturbation and the perturbation after an e-folding time in Mathematica. The e-folding time in physical units is ~6 Myr, and in computational units corresponds to t = 0.0016.  
 
 
@@ -164 +168 @@
 t=1/omega
 
-These next plots are what I would expect AstroBEAR should give us after 1) strictly initializing a sinusoidal density perturbation, and 2) allowing it to evolve in time with self-gravity turned on. These results are as follows:
+These next plots show AstroBEAR's output using density, velocity, and pressure perturbations described earlier:
 
-[[Image(rhoFinalAbear.png, 35%)]]t=0
+[[Image(JeansInit23July2013.png, 35%)]]t=0
 
-[[Image(rhoFinal2Abear.png, 35%)]]t=1/omega
+Vx is in red, rho is in green. The density peaks at the zero's of Cos(kx). E.g., a local max is at 1. The vx perturbation is a Sin(x) function, and it has minima that corresponds with the density maxima. This produces converging flows at the max in density, as you would expect you need to develop the Jeans instability.
 
-These are using periodic physical and elliptical BCs.
+[[Image(JeansFinal23July2013.png, 35%)]]t=5/omega
 
-Now, a query-over-time of rho at r = (1,0,0) produces the following output:
+By the end of the sim, the density perturbation has grown a little, but velocity has grown a lot.
+
+(These are using periodic physical and elliptical BCs, and an ideal EOS with gamma = 1.0001).
+
+Now, a query-over-time of rho at r = (1,0,0) produces the following output when compared to the analytical result:
+
+[[Image(GrowthRate.png, 35%)]]
+
+Pretty tight fit!
 
 
-At t=0.0016
 
-[[Image(expRho1.png, 35%)]]
-
-And at t=0.005:
-
-[[Image(rho0time.png, 35%)]]
-
-It looks like exponential growth... 
-
-Makes me wonder:
-
-1) Scaling error?
-
-2) Error in analytic function at t=6 Myr?
-
-Here's the last curiosity, when I look at the frame where the density = e*rhoInit, the peaks match the 'analytical function' I plotted in Mathematica, but the valleys don't. . 
-
-[[Image(rhoE.png, 35%)]] 
-
-
-[[Image(RhoFinal.png, 35%)]]
-
-