Changes between Version 49 and Version 50 of u/erica/RoeSolver

Timestamp:

05/16/13 16:46:33 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -44 +44 @@
 }}}
 
-The eigen values and vectors are derived straightforwardly from the Jacobian, using typical methods.
+The eigenvalues and vectors are derived straightforwardly from the Jacobian, using typical methods.
 
-Now, we can either assume the independent variables u, rho, etc. of these functions for alpha, lambda, and K are 1) reference states which we set, or 2) some general averaged versions of the variables, which we have to solve for. Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows.
+Now, we assume the independent variables u, rho, etc. of these functions for alpha, lambda, and K are reference states (associated with hat notation) which we use to solve for any general, averaged versions of the variables (associated with tilde notation). Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows.
 
 = Roe-Pike Approach for Euler Equations = 
 
-For the x-split, 3-dimensional Euler equations, we have the following eigen values and vectors:
+For the x-split, 3-dimensional Euler equations, we have the following eigenvalues and vectors:
 
 {{{#!Latex
@@ -60 +60 @@
 
 {{{#!Latex
-\vec{K}^1 = <1, u-a, v, w, H-ua>, ~\vec{K}^2 = <1,u,v,w,V^2/2>, ~\vec{K}^3 = <0,0,1,0,v>, ~\vec{K}^4 = <0,0,0,1,w>, ~\vec{K}^5 = <1, u+a, v, w, H+ua> 
+\vec{K}^1 = <1, u-a, v, w, H-ua>,
+}}}
+{{{#!Latex
+ \vec{K}^2 = <1,u,v,w,V^2/2>,
+}}}
+{{{#!Latex
+\vec{K}^3 = <0,0,1,0,v>, 
+}}}
+{{{#!Latex
+\vec{K}^4 = <0,0,0,1,w>, 
+}}}
+{{{#!Latex
+\vec{K}^5 = <1, u+a, v, w, H+ua> 
 }}}