Changes between Version 10 and Version 11 of HydroStaticStar

Timestamp:

10/17/12 14:15:46 (12 years ago)

Author:

idilernia

Comment:

—

HydroStaticStar

@@ -62 +62 @@
 this simpler form can be applied to our profile array, you can check the [wiki:Profiles Profiles] page to see how this is done. After we created this abstraction of a column of gas in hydrostatic equilibrium, we can use interpolation to port this 1D object to a 2D or 3D model.
 
-== 2D vs 3D ==
+== 2D,3D and Softening ==
 
-[[Image(2Dvs3D.png, 1000px)]]
+Due to steep changes in density and gravitational potential close to the center of mass of a star, the point gravity in this model, some softening of these two parameters is needed.[[BR]]
+With !PlummerSoftening being used to soften the gravitational potential and force in this module, a difference in the pressure and temperature profile arise between 2D and 3D models.[[BR]]
+You can see how the gravity force varies between 2D and 3D:[[BR]]
+2D:
+{{{
+GravityForce=-PlummerSoftening2D*mass*ScaleGrav
+PlummerSoftening2D=2d0*pos/(sum(pos(1:nDim)**2)+r_soft**2)
+}}}
+3D:
+{{{
+GravityForce=-PlummerSoftening*mass*ScaleGrav
+PlummerSoftening=pos/((sum(pos**2)+r_soft**2)**(1.5d0))
+}}}
+[[BR]]
+Clearly, the 3D model shows a steeper gradient in pressure.[[BR]]
+The plot below indicates how the pressure gradient changes between 2D and 3D models and how it has important repercussions on the temperature profile as well.[[BR]]
+[[Image(2Dvs3D.png, 400px)]]
 
 == Refence model comparison and results ==
 
-[[Image(wiki:HydroStaticStar:plotshse2.png, 800px)]]
+We divided the checking of our model accuracy into two stages:
+1) comparing module profiles with reference models in the literature
+2) running the model
 
-[[Image(3Dhse.gif, 800px)]]
+For the first testing stage, the density profile of an AGB star (can be found [http://www.public.iastate.edu/~sdk/models/ here]) was loaded into the module, after calculating pressure and temperature profiles needed for an HSE condition, the generated profiles were compared with the reference model.[[BR]]
+The following plot below compares the two models:
+
+[[Image(wiki:HydroStaticStar:plotshse2.png, 400px)]]
+
+In the second testing stage, the model was run to check for changes in velocity.[[BR]]
+Clearly, the outcome that can be expected from an equilibrium condition is the absence of change in velocity. In the case of an equilibrium at rest, we would expect our model not to change over time.[[BR]]
+Below is the density, pressure, temperature and mach profiles for our model.[[BR]]
+[[Image(3Dhse.gif, 400px)]]