Changes between Version 55 and Version 56 of u/erica/CoreCollapseBlog

Timestamp:

04/17/18 16:09:19 (7 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/CoreCollapseBlog

@@ -33 +33 @@
 ==== Checking HSE after interpolation of profile onto mesh: ====
 
-As shown below (post from 3/15), the profiles generated by AstroBEAR's HSE module closely match the input progenitor profiles, which are in HSE. How well the actual simulation matches the input progenitor profile (i.e. following Interpolation onto the mesh) depends on the resolution. The following line plot shows that increasing the resolution by a factor of 8 (blue curve) improves the accuracy of the HSE solver -- the sphere reaches HSE over much smaller region in the higher resolution case rather than the lower resolution run. It seems HSE is achieved by about 30 grid cells on the finest mesh -- thus, want to minimize the physical distance these cells take up within the sphere. 
+As shown below (post from 3/15), the profiles generated by AstroBEAR's HSE module closely match the input progenitor profiles, which are in HSE. How well the actual simulation matches the input progenitor profile (i.e. following interpolation onto the mesh) depends on the resolution. The following line plot shows that increasing the resolution by a factor of 8 (blue curve) improves the accuracy of the HSE solver -- that is to say the sphere reaches HSE over much smaller region. From this plot, it seems HSE is achieved by ~30 grid cells on the finest mesh. At the present resolution ($dx\approx .0019~(CU)$) this corresponds to $\approx .1 R_{sphere}$
 
 [[Image(HSE_octant_resolutionStudy.png, 35%)]]
 
-At an effective resolution of ~$dx = .0019$, the sphere is very close to HSE within .1 of its radius.
-
-HSE here is defined as the difference of the magnitude of the gravitational and pressure acceleration:
+Note, HSE is defined here as the difference of the magnitudes of the gravitational and pressure accelerations:
 
 $HSE =   mag[\nabla \phi_g] - mag[ \frac{\nabla P}{\rho} ]$