Changes between Version 36 and Version 37 of u/erica/GudonovMethodEuler

Timestamp:

05/06/13 12:10:07 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/GudonovMethodEuler

@@ -70 +70 @@
 === Sampling the solution === 
 
-Once Pstar is found to within a certain degree of accuracy, ustar is given immediately by a simple formula in Toro, chapter 4. 
+Once Pstar is found to within a desired degree of accuracy, ustar is given immediately by a simple formula in Toro, chapter 4. These quantities are used to determine the combination of waves present along the intercell boundary. Once these are determined, we look for the speeds of the wave, relative to the grid speed, dx/dt = 0, which corresponds to the local intercell boudary. Depending on where the waves are, relative to this interface, the algorithm prescribes a density, velocity, and pressure for the boundary. These quantities are then used to update the cells, as described above.
 
-The time-step, is constrained by the CFL condition, which uses the max wave speed on the grid. The constraint used in the God. code here allows any given wave on the grid to travel a full delta_x in a time-step. In allowing this, we achieve a more efficient time-marching scheme, but with the assumption that wave interactions do not lead to wave accelerations.
+=== Constraining the time step === 
+
+The time-step, is constrained by the CFL condition, which uses the max wave speed on the grid. The constraint used in the God. code here allows any given wave on the grid to travel a full delta_x in a time-step. In allowing this, we achieve a more efficient time-marching scheme, but with the assumption that wave interactions do not lead to wave accelerations. The CFL condition is given by:
+
+{{{#!Latex
+
+CFL = smax/(dx/dt)
+
+}}}
 
 == The code ==