Changes between Version 1 and Version 2 of HydroStaticStar

Timestamp:

10/16/12 13:51:00 (12 years ago)

Author:

idilernia

Comment:

—

HydroStaticStar

@@ +1 @@
+= !HydroStatic Star =
+
+== Purpose ==
+
+This module aims to reproduce a situation of hydrostatic equilibrium (HSE), a condition where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force.
+
+[[Image(Hydrostatic_equilibrium2.png, 250px)]]
+
+we can translate the image above into the condition:
+
 {{{
 #!latex
-\frac{dP}{dh} = - \rho(h)\cdot g(h) \\
+\frac{dP}{dh} + \rho \cdot g = 0\\
 }}}
+
+= Implementation =
+
+Two fundamental objects are used by this module:
+- [wiki:AmbientObjects Ambients]
+- [wiki:Profiles Profiles]
+- PointGravity
+
+For this module, the first step to recreate the solution is to determine a 1D profile in hydrostatic equilibrium, this profile can then be applied to a spherically symmetric 3D model using interpolation. [[BR]][[BR]]
+With a little bit of imagination we can think of a 1D column of gas as an array of values:
+
+||COLUMN TOP||
+
+||h,,5,,||ρ,,5,,||P,,5,,||
+||h,,4,,||ρ,,4,,||P,,4,,||
+||h,,3,,||ρ,,3,,||P,,3,,||
+||h,,2,,||ρ,,2,,||P,,2,,||
+||h,,1,,||ρ,,1,,||P,,1,,||
+||h,,0,,||ρ,,0,,||P,,0,,||
+
+||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).