I have a 3D solver wherein I want to implement dual time stepping, so that the code has the capabilities for compressible, unsteady flows. Presently the code has DTS for Incompressible flows, based on the Weiss and Smith scheme.

I am basically extending the same schem for the compressible flow, for considering the preconditioning matrix as a unity matrix and updating in conserved variables instead of primitve as in Weiss.

While I am implementing the scheme, i have a few doubts. 1. the no. of subiterations, so that i get a converged solution for pseudo time step to get time accuracy at the physcial time step. And the computing time is less than what i will get with the global time step, so that DTS is justified. 2. the value of the physical time step. since the CFL condition will be applied to the pseudo time. 3. is it justified if sub-iterations are exlicit. coz almost everyone have discretized implicitly.

My code is finite volume, multi block, structured, without multi grid. I wuld really appreciate any comments.

Aditya

Dear Aditya,

I have replied in detail to your earlier post on Friday under the title of Dual time steppin, a little don in the message list.

Regards,

Ganesh

You also have to worry about stability, depending on the situation finite differences is sometimes more stable than the finite element method. Also depends on whether or not you are working with a unstructured or structured grid.

~Tiger

Dear Ganesh,

According to Jameson's work, we treat the unsteady residual as convective and dissipative parts. Then, in which part do source terms (which are constant during R-K iteration) and 3W/2dt term take place? in dissipative part? Can anyone please explain in detail?

Best regards

CFD Student

Dear CFD student,

In Jameson's work, he utilises multigrid for acceleartion convergence in DTS and also artificial dissipation to reduce spurious oscillations. As mentioned in his paper, from considerations of linear stability, the residual is split into convective and dissipative parts. Now you would see that the residual, R* contians R on the RHS, which has contribution from convective fluxes as well as from artificial dissipation(added). It is this splitting that arises in R* also. The source terms and 3w/2delt terms can be still taken to be on convective side. In fact, they come out of the construction of the pseudo-steady problem and strictly belong to the Backward Differncing of real time, so there is no point in making any classifiaction. As far as the multigrid is concernerd, the beta terms should be applied to the dissipative part and not on any of these terms, which I hope is what you wanted to know. In any case, if you are employing flux limiters you could get away with the artificial disspation and the related operations, which would possibly make things easy.

Hope this helps

Regards,

Ganesh

Dear Ganesh,

Thanks for your explanatin. It is very helpful.

Best regards.

CFD Student