Changes between Version 63 and Version 64 of SelfGravityDevel

Timestamp:

10/22/19 11:18:56 (5 years ago)

Author:

Jonathan

Comment:

—

SelfGravityDevel

@@ -1 +1 @@
 = Self Gravity =
-
-(This is a skeleton while a new version of this page is under construction.)
 
 == Physics ==
 === Poisson Equation of Self Gravity ===
 
-  The electric field generated by a point charge[[latex($Q$)]]is
+The inclusion of self gravity involves an additional force to the momentum equation
+
+[[latex($\frac{d \rho \mathbf{v}}{dt} = \mathbf{f}_g = -\rho \nabla \phi$)]]
+
+and energy equation
+
+[[latex($\frac{d E}{dt} = \mathbf{v} \cdot \mathbf{f}_g = -\rho \mathbf{v} \cdot \nabla \phi$)]]
+
+and requires the solution for the gas potential
+
+[[latex($\nabla^2 \phi = 4 \pi G \left (\rho - \rho_0\right)$)]]
+
+where 
+
+* [[latex($\rho_0 = \bar{\rho}$)]] for periodic boundary conditions 
+* [[latex($\rho_0 = 0$)]] otherwise.
+
+
+AstroBEAR uses hypre's linear solver to solve Poisson's equation for the potential.  However, there are two methods for including the source terms for momentum and energy.  The non-conservative approach simply includes the terms during a source update, while the conservative approach recasts the RHS of the momentum and energy equations as total divergences - so they can be differenced conservatively.
+
+
+
+
+
+The electric field generated by a point charge[[latex($Q$)]]is
 
  [[latex($E=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}$)]]