Changes between Version 67 and Version 68 of u/erica/RoeSolver

Timestamp:

05/17/13 16:50:12 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -16 +16 @@
 
 {{{#!Latex
-\vec{U}_t + \frac{\partial \vec{F}} {\partial \vec{U}} \vec{U}_x = \vec{0}
+\vec{U}_t + \frac{\partial \vec{F}} {\partial \vec{U}} ~\vec{U}_x = \vec{0}
 }}} 
 
@@ -22 +22 @@
 
 {{{#!Latex
-\hat{A} = \frac{\partial \vec{F}}{\partial \vec{U}} 
+\hat{A} = \frac{\partial ~\vec{F}}~{\partial ~\vec{U}} 
 }}}
 where, A-hat is a Jacobian matrix of averaged/constant values, we can derive an expression for the numerical flux in terms of 1) wave strengths (alpha), and the 2) eigenvalues (lambda) and 3) right eigenvectors (K) of the 'averaged' Jacobian:
@@ -124 +124 @@
 
 {{{#!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>
+\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>
+\vec{K}^{(3)} = <1, ~u+a, ~H+ua>
 }}}