Hi,

Local time-stepping can be used to accelerate convergence towards a steady state solution. The steady state is reached when the diffence in values of to successive solutions is small. However, time steps being chosen locally, the time for the steady state solution then loses its physical meaning. The question I am asking? Is it possible and useful to perform time accurate local time-stepping in transient computations? Does anybody know any references in regards to this matter?

Many thanks.

Pierre-Yves Lesage

Hi Pierre-Yves,

There's a time-advancement scheme called "dual time stepping" method that adopts one pseudo-time variable and one real time variable. The pseudo-time is used for the inner iterations and local time stepping can be still used there.

To answer your question, obviously we cannot get time-accurate solution unless same time step is used for every cell. It's expensive, but is justified since in many applications the temporal resolution of unsteady flow in question requires use of sufficiently small time step. In that sense, it's useful.

In "dual time stepping" method, the pseudo time step is local time. The dual time method is: Put the real time step into the source term and then solve the new equations using loacal time step. You can read the following two papers for details: 1. Alonso, J. and Jameson, A. "Fully-Implicit Time-Marching Aeroelastic solutions", AIAA paper 94-0056 2. Gaitonde, A. L., " A Dual-Time Method for solution of the Unsteady Euler Equations", Aeronautical Journal, Oct. 1994.