Dual time stepping makes euler vortex go slower?

General
1

Hi, everyone.

I just tested the dual time stepping for euler vortex case in the examples using following *.ini configuration:

[solver-time-integrator]
formulation = dual
scheme = bdf2
pseudo-scheme = tvd-rk3
tstart = 0.0
tend = 100.0
dt = 1
pseudo-dt = 0.01
controller = none
pseudo-niters-max = 20
pseudo-niters-min = 5
pseudo-aresid = 1e-5
pseudo-rresid = 1e-5

It is really fast (4s) comparing with standard time integrator (39s).

100.00/100.00 ela: 00:00:04 rem: 00:00:00

However, the result is different from default setting. The vortex goes lower in the dual-time stepping case.

dual:

std:

I also tried to use pseudo-dt = 0.05 and 0.1 but it resulted in NaN error. My question is:

  1. What is wrong with this euler-vortex case using dual time stepping?

  2. What can I expect from using dual-stepping?

2

Hi!

A. The difference between the results is resulting from the lack of convergence. Since you have specified your real time step a hundred times larger than your pseudo time step, it is unlikely that 20 iterations (your max) would be sufficient to converge each pseudo steady state (that is each real time step).

B. Dual time stepping can be used as an acceleration method when used together with a fast steady state solver. It was added to accommodate for instance the method of artificial compressibility (incompressible Navier-Stokes), which is included in the next release.

Best regards,

Niki