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RoeSolver

v93	v94
35	35	[[latex($\triangle \vec{U} = \vec{U}_R - \vec{U}_L = \Sigma _{i=1,m} \hat{\alpha}_i(\vec{W}) \hat{\vec{K}}^{(i)}(\vec{W})$)]]
36	36
37		The eigenvalues and vectors are derived straightforwardly from the Jacobian, using typical methods.
	37	where the W-vector denotes the vector primitive variables rho, u, and p, as usual. The eigenvalues and vectors are derived straightforwardly from the Jacobian, using typical methods.
38	38
39	39	Now, we assume the independent variables u, rho, etc. of these functions for alpha, lambda, and K are reference states (associated with hat notation) which we use to solve for any general, averaged versions of the variables (associated with tilde notation), which we use in the numerical flux. Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows.