Changes between Version 36 and Version 37 of u/erica/RoeSolver


Ignore:
Timestamp:
05/16/13 15:59:41 (11 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RoeSolver

    v36 v37  
    4646The eigen values and vectors are derived straightforwardly from the Jacobian, using typical methods.
    4747
    48 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 alebraic analysis for the case of the Euler equations. The results are as follows:
     48Now, 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.
     49
     50For the x-split, 3-dimensional Euler equations, we have the following eigen values and vectors:
     51
     52{{{#!Latex
     53\lambda_1 = u-a, \lambda
     54}}}
     55
     56
    4957
    5058= A Sample Algorithm =