Changes between Version 37 and Version 38 of u/erica/CylindricalGravity

Timestamp:

05/19/15 16:31:00 (10 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/CylindricalGravity

@@ -1 @@
-=== Self Gravity in astrobear ===
+== Self Gravity in astrobear ==
 
-The governing equation is Poisson's equation for gravity, which for a given mass distribution can be solved for the gravitational potential. In astrobear, we use the potential to solve for the gravitational forces in the fluid. The equation we use for the resultant force is either in conservative or non-conservative form (want to read more into the numerical methods here and link to these pages).
+The governing equation is Poisson's equation for gravity, which for a given mass distribution can be solved for the gravitational potential. In astrobear, we use the potential to solve for the gravitational forces in the fluid. 
 
-== Description of why we want 2.5D self gravity ==
+== Multidimensions ==
+
+Poisson's equation can be simplified (i.e. written with last terms) under various symmetries in the problem setup. Some examples are:
+
+2D-symmetry-- Can drop the z-derivative term in the PDE. This modified equation is appropriate for an infinite slab. The variables in the PDE are x & y. [[br]]
+
+2.5D-symmetry--  Use cylindrical geometry to rewrite the PDE, and drop the theta derivative terms. This is appropriate for cylindrical symmetry. The variables are r & z.
+
+If the simulations have these symmetries, then instead of solving Poisson's full 3D equation, we can solve a modified, simpler equation. 
+
+== 2.5D Geometry ==
+
+2.5D means cylindrical symmetry, i.e. the xy plane now represents the rz plane -- there is azimuthal symmetry in phi.
+
+The hyperbolic solvers for the Euler equations have been modified (i.e. include 1/r terms now), however, up until this fix in the code, any calculations with gravity used regular 2D gravity, which would introduce errors. Here is an example: