Changes between Version 73 and Version 74 of u/erica/GudonovMethodEuler

Timestamp:

05/08/13 11:45:17 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/GudonovMethodEuler

@@ -15 +15 @@
  [[Image(God.png, 75%)]]
 
-In this picture, WL and WR denote the arrays of primitive fluid variables (namely, rho, u, P) designated as the values of those variables at the adjacent cell centers, the asterisk (*) indicates a star region that is bound by two outgoing arrows, the arrows indicate the wave pattern generated in the LRP, F is the numerical flux (described below), and the conservative formula is given by the Godunov scheme, also presented below.
+In this picture, WL and WR denote the arrays of primitive fluid variables (namely, rho, u, P) designated as the values of those variables at the adjacent cell centers (here at cell=i-1 and i), the asterisk (*) indicates a star region that is bound by two outgoing arrows, the arrows indicate the wave pattern generated in the LRP, F is the numerical flux (described below), and the conservative formula is given by the Godunov scheme, also presented below.
 
 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) 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