Changes between Version 35 and Version 36 of u/erica/MusclHancock

Timestamp:

06/18/13 12:49:14 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/MusclHancock

@@ -85 +85 @@
  [[Image(evolve.png, 35%)]]
 
-3. 
- 
+3. Solve the new Riemann problem
+
+  [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]]
+
+
+  [[latex($ u(x,0) =  \{ ^{\bar{u}_i^r,~~~~ x <0}_{\bar{u}_{i+1}^l, ~~x>0} $)]]
+
+  using the evolved extrapolated boundary values. The solution of this problem is then used in the Godunov flux, which is used in updating cell i. Recall the Godunov flux is simply, 
+
+  [[latex($ f_{i+1/2} = f(u_{i+1/2}(x/t=0))$)]]
+
+  i.e. the numerical flux at the intercell boundary equals the physical flux evaluated at the similarity solution of the LRP (local Riemann Problem) at that boundary.
  
 
+At this point, we are left with a higher order accurate code, but not one that is free of spurious oscillations near large gradients. To circumvent this, we need to add a TVD measure. There are some different ways of doing this, i.e. limited slopes, flux-limiters, and slope limiters. Here we focus on slope limiters. 
 
-  
-
-  
-
-At this point, we are left with a higher order accurate code, but not one that is free of spurious oscillations near large gradients. To circumvent this, we need to add a TVD measure.
+= Slope Limiters = 
 
 = Algorithm Outline =