Changes between Version 23 and Version 24 of u/erica/GudonovMethodEuler

Timestamp:

05/04/13 14:33:15 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/GudonovMethodEuler

@@ -10 +10 @@
 4. Solve these local RP's, and use solution to compute fluxes
 
+
+
+5. Use these fluxes to update cells.
+
+Here is a picture of the situation:
+
  [[Image(God.png, 35%)]]
 
-5. Use these fluxes to update cells.
+If we were to blow the left star region up (on the intercell boundary between cell i-1 and i), what we would have is 3 non-linear waves (contact, shock(s) and/or rarefaction(s)) being generated at this boundary IF the left and right states (WL and WR, where W is the array of primitive variables) were different. If these states are the same, then NO non-linear waves would be generated. We would like to first find pstar, the value of pressure between the left and right waves, in the region so-called the "star region". Once this is known, we can determine the types of waves generated. Since they are propagating away from the intercell boundary, the exact values of the fluid variables along the intercell boundary depend on their relative speeds. We then would sample the solution to the LRP, along this boundary only. Once we have found the solution at this boundary, given by
+
+{{{#!Latex
+\rho_s, \p_s, \u_s
+}}}
+
+we compute the flux at this boundary. These fluxes are the fluxes of the Euler equations, in conservation form. That is, 
+
+
 
 == The method ==