About the MUSCL scheme for compressible simulations
I am studying the MUSCL (finite difference) scheme with the Steger-Warming splitting to solve compressible flows. One step is not clear for me.
The scheme is
U(n+1)_i,j=U(n)_i,j - dt/dx(F_i+1/2,j-F_i-1/2,j) (1D case)
where F can be split into two parts. For example F_i+1/2,j= F^+_i+1/2,j + F^-_i+1/2,j
Further, F^+_i+1/2,j=F^+(U_i+1/2,j_L), F^-_i+1/2,j=F^-(U_i+1/2,j_R)
If we go inside to the expression of F^+(U_i+1/2,j_L), we see that it is expressed by the components of U_i+1/2,j_L and the eigenvalues of the coef matrix. My question is how to evaluate these eigenvalues? Shall I use to Roe average (between grid i and i+1) or just use the components of U_i+1/2,j_L to get u, u+a and u-a as these eigenvalues?
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