Changes between Version 45 and Version 46 of 1DPulsedJets

Timestamp:

03/30/12 12:31:53 (13 years ago)

Author:

ehansen

Comment:

—

1DPulsedJets

@@ -215 +215 @@
 
 == 1D Radiative Shock Simulations ==
-These simulations follow Ch. 4 of Delamarter '01 and his treatment of the 1D "steady" radiative shock problem.  The purpose of this problem is to check that the cooling source terms are being handled correctly.  Here are some useful links:
+These simulations follow Ch. 4 of Delamarter '01 and his treatment of the 1D steady radiative shock problem.  The purpose of this problem is to check that the cooling source terms are being handled correctly.  Here are some useful links:
 
 [http://www.pas.rochester.edu/~bearclaw/delamarterplots.html AstroBEAR 1.0 test page]
@@ -222 +222 @@
 
 === Equations ===
-
+The shock jump equations for a stationary shock are used to solve for the initial post-shock values.  The post-shock velocity v2 can be written as:
+
+
+where v1 is the ambient velocity, and M is the ambient mach number.  Remember that the mach number M = v1/c where c is the ambient sound speed, and c = sqrt(gamma*p1/rho1) where p1 is ambient pressure, and rho1 is ambient density.
+
+The post-shock density and pressure (rho2 and p2 respectively) can be found by using mass flux and momentum flux conservation across the shock:
+
+These post-shock values become the boundary conditions for the fluid equations in the cooling region:
+
+where rho, v, and p represent the density, velocity, and pressure in the cooling region as functions of x, and lambda is the cooling rate.
+
+[[BR]]
 === Initial Parameters ===
-
+n1 = 60 particles/cc
+v1 = 10^7^ cm/s
+T1 = 10^4^ K
+
+For analytic cooling,
+[[latex($\Lambda = n^{2}*\alpha*T^{\beta}$)]]
+where n and T and the number density and temperature in the post-shock region respectively.
+
+For these simulations,
+
+beta = 2
+alpha = 1.2345 * 10^-34^ erg*cm^3^/s/K^2^
+
+cell length = 10^18^ cm
+problem domain = 400 cells
+final time ~ 4000 years
+
+[[BR]]
 === Results ===