[Shenren_CN]

I'm learning how to implement a pre-conditioner for a compressible flow solver. I have one question about the time stepping, when a Weiss-Smith pre-conditioner is used.

So our solver is a steady flow solver, and originally local time stepping was used with multistage RK time integration. After I implemented the preconditioner (to rescale the residuals by multiplying the original residual with several matrix associated with the pre-conditioner), what change do I need to make to the time step calculation? Do I need to change the convection jacobian radius according to the pre-conditioned system (adjusted sound speed, which is close to typical flow speed) or should I keep them as they were? Does the answer depend on which kind of flux scheme I'm using (JST, Roe, AUSM+, Van Leer flux splitting)?

Thanks.