Changes between Version 3 and Version 4 of u/erica/RoeSolver


Ignore:
Timestamp:
05/15/13 23:50:21 (11 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RoeSolver

    v3 v4  
    99U_t + F(U)_x = 0
    1010}}}
    11 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:
     11where, 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:
    1212
    1313Where now the Jacobian is an averaged matrix, representing constant coefficients for the Euler equations.