48 | | 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). Toro goes through the algebraic analysis for the general case for the Euler equations. The results are as follows. |

| 48 | 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. |