Roe implement about preconditioning

ricklee

Dear all:

I used weiss and smith's preconditioning in my

compressible code. But I still confused about the Roe

scheme.

Original Roe: F = 0.5*(F_L+F_R)+0.5*abs(A)*(U_R-U_L)

preconditioning: F = 0.5*(F_L+F_R)+0.5*P*abs[(P^-1)*A]*(U_R-U_L)

or F = 0.5*(F_L+F_R)+0.5*P*abs[(P^-1)*A*M]*(Up_R-Up_L)

here

M = partial(U)/partial(Up)

U = [rho rho*U rho*E]

Up = [P U T]; T = P/rho

Which is correct for preconditioning?