Changes between Version 62 and Version 63 of u/erica/RoeSolver

Timestamp:

05/17/13 16:39:24 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -121 +121 @@
 }}}
 
+This vector equation has the following components for the 3D Euler equations,
+
+{{{#!Latex
+\vec{F}_{i+1/2} = <\rho_{i+1/2}, u_{i+1/2}, p_{i+1/2}>
+}}} 
+
+{{{#!Latex
+\vec{F}_L = <\rho_L, \rho_L * u_L, 0.5\rho_L*u_L^2 + \frac{p_L}{\gamma - 1}>
+}}} 
+
+{{{#!Latex
+\vec{K}^{(1)} = <1, u-a, H-ua>
+}}} 
+
+{{{#!Latex
+\vec{K}^{(2)} = <1, u, 0.5 u^2>
+}}}  
+
+{{{#!Latex
+\vec{K}^{(3)} = <1, u+a, H+ua>
+}}} 
+
 The results for the method are the following equations for the wave-speeds:
 
@@ -145 +167 @@
 along with their corresponding expressions for the rho, u, v, w, H, and a (listed in Toro, eqn. 11.118) that we would plug into these wave speeds and the above expressions for the eigenvalues and eigenvectors. These in turn would be used in the numerical flux for the Godunov method. 
 
-Note the definition
+Note in the above formalism, the following definition is used,
 
 {{{#!Latex