Changes between Version 34 and Version 35 of u/erica/RoeSolver

Timestamp:

05/16/13 15:48:20 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -38 +38 @@
 = The Roe-Pike Approach = 
 
+This approach avoids construction of an averaged Jacobian. Instead the method involves solving for the eigen values and vectors for the original Jacobian, deriving an expression for the wave speeds, and then evaluating these expressions using some vector of averaged scalar quantities, typically W, averaged. So from the equation above of the Euler equations in Jacobian form, we can derive the equations for wave speeds:
+
+{{{#!Latex
+\triangle \vec{U} = \vec{U}_R - \vec{U}_L = \Sigma _{i=1,m} \alpha_i \vec{K}^(i)
+}}}
+
 = A Sample Algorithm =