Changes between Version 18 and Version 19 of u/erica/RoeSolver

Timestamp:

05/16/13 14:25:33 (12 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/RoeSolver

@@ -16 +16 @@
 \vec{U}_t + \frac{\partial F} {\partial U} \vec{U}_x = 0
 }}} 
-where, the Jacobian matrix A= is a NON-constant coefficient matrix, the Euler equations comprise a NON-linear set of equations. An easier system to solve would be one that is a linear, constant coefficient system of equations. We can transform the Euler equations into this simpler case, if we make transformations of variables in the matrix to be some average function of the left and right data state variables. This results in the set of equations:
+
+If we assume that \partial where, the Jacobian matrix A= is a NON-constant coefficient matrix, the Euler equations comprise a NON-linear set of equations. An easier system to solve would be one that is a linear, constant coefficient system of equations. We can transform the Euler equations into this simpler case, if we make transformations of variables in the matrix to be some average function of the left and right data state variables. This results in the set of equations:
 
 Where now the Jacobian is an averaged matrix, representing constant coefficients for the Euler equations.