Hi all,

I have a question on "dual-time stepping" technique. Simply, why? What is the advantage? You solve a steady-state problem at every real-time step, which can take very long. Yes, you can use preconditioning or multigrid etc, but what is the point of creating a steady-state problem and solving that.

I really want to know the reason why dual-time stepping has its place.

Thank you Dave

Dual time-stepping is useful for implicit, unsteady calculations. See the following http://aero-comlab.stanford.edu/Pape...afosr.2003.pdf

Thanks Praveen, I have just read page 17 of Jameson's slides.

As I understand, in order to use a much larger time step dt in the time marching, an implicit scheme is employed. However, the implicit formulation i.e. equation (4) is difficult to solve. In order to solve the implicit equation (4) to obtain w(n+1), an artificial time t* is introduced and w(n+1) is treated as a steady state solution of the equation (5).

In order to solve the equation (5), an explicit artificial time marching is used, How large the artificial time step dt* can be used depends on the stability of equation (5).

The time accuracy of the original problem depends on the real time step dt.

Please correct me if my understanding is wrong.

Li Yang

Treat flow solution of t+1 as the steady-state, from a initial flow solution at t, requires several (<5) subiterations to achived the required time accuracy. That is the hoped performance of dual time stepping. Why use dual time stepping? some numerical schemes contain factorization error, time-accuracy is not exactedly meeted if solved once. However, The merit of dual time steeping depends on the subiteration procedure. One may naively think it needs only a few subierations from T to T+1 as the two flow fields are so close. But things are not so simple, especillay coupled with nonlinear boundary condition. A residual drop of 1-2 order is quickly reached, but further 4-5 orders reduction in residual is very difficult to attain within acceptable iteration numbers. SO you need develop good preconditioning iterative proceudre when using dual-time steeping.

ok, the explanation in the Jameson's presentation was the mathematical explanation. Can anyone explain me what is the physics behind it? why does the duel time stepping solves it faster and why it is required? might look like a dumb questions to some people but its still a puzzle for me.

J-