Changes between Version 45 and Version 46 of u/erica/RoeSolver

Timestamp:

05/16/13 16:32:08 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -93 +93 @@
 }}}
 
-Recall,
+Recall that the numerical flux is given by,
 
 {{{#!Latex
-\vec{F}_{i+1/2}= \frac{1}{2}(\vec{F}_L + \vec{F}_R) - \frac{1}{2}\Sigma_{i=1,m} \alpha_i \lambda_i \vec{K^{(i)}}
+\vec{F}_{i+1/2}= \frac{1}{2}(\vec{F}_L + \vec{F}_R) - \frac{1}{2}\Sigma_{i=1,m} \tilde{\alpha}_i \tilde{\lambda}_i \tilde{\vec{K^{(i)}}}
+}}}
+
+where the tilde's are the solution of the Roe approach, and are given by:
+
+{{{#!Latex
+\tilde{\alpha}_i = \hat{\alpha}_i(\tilde{\vec{W}}), ~\tilde{\lambda}_i = \lambda_i(\tilde{\vec{W}}), ~\tilde{\vec{K}^{(i)}} = \vec{K}^{(i)}(\tilde{\vec{W}})
 }}}