Changes between Version 2 and Version 3 of HydroStaticStar

Timestamp:

10/16/12 14:34:39 (12 years ago)

Author:

idilernia

Comment:

—

HydroStaticStar

@@ -13 +13 @@
 \frac{dP}{dh} + \rho \cdot g = 0\\
 }}}
+
+where dP/dh is the change in pressure with respect to height, ρ is density and g is the gravitational potential.
 
 = Implementation =
@@ -35 +37 @@
 ||COLUMN BASE||
 
-We can relate each level of the column to an position in an array which contains height (h), density(ρ) and pressure(P).
+We can relate each level of the column to an position in an array which contains height (h), density(ρ) and pressure(P), that is:
+
+{{{
+    REAL(KIND=qPREC), DIMENSION(100,3) :: column !where the first indexing is the level 
+                                                 !2nd indexing determines the attribute (1 height, 2 rho, 3 pressure)
+}}}
+
+In this specific implementation, a density profile needs to be specified by the user, the module will be able to calculate the ideal pressure in order to create an HSE solution.
+
+In order to calculate the ideal pressure, we need to interpret:
+
+{{{
+#!latex
+\frac{dP}{dh} = - \rho \cdot g\\
+}}}
+
+in a discrete way, this gives:
+
+{{{
+#!latex
+P(h) = P(h+\Delta h) + g(h)\cdot\rho(h)\cdot\Delta h
+}}}
+
+let's translate this condition under the form of the array specified above:
+
+{{{
+#!latex
+
+P(h) \rightarrow col(i,3)\\
+P(h+Δh) \rightarrow col(i+1,3)\\
+g(h) \rightarrow GravityForce \\
+\rho(h) \rightarrow half*(col(i,2)+col(i+1,2))\\
+Δh \rightarrow col(i+1,1)-col(i,1)\\
+}}}