Hi all,
I am looking for some scientific exchange with researcher that have developed or even used an implicit 2d RANS solver.
I have there following questions in this context ....
1. Which numerical methods is used?
2. How is positivity treated in the implicit world?
3. What kind of equations solver is used?
4. How did the parallelization worked out?
In the literature for this problem is very limited, I know two papers, where on of those is only 1st order in space and time.
Cheers
Aron
There are some things in your question that should be clarified.
- Are you asking for the URANS formulation? RANS is a steady formulation by definition.
- What should be the relevance in high order numerical method using URANS? The turbulence model has a larger impact (greater magnitude order) than the local truncation error. Then, the time variability in URANS is constrained by the resolved external forcing, there is no need to use higher order time integration.
Hi everybody,
indeed it needs more clarification, now let's call it URANS 1st. Then, we need implicit schemes to overcome severe CFL constraint, since the time scales of interest are much greater than the stability time scales based on the CFL conditions. With respect to the order I wanted to have higher than one in all spaces, while the scheme must preserver positivity of the water depth.
Moreover, some more remarks ...
1. Method should use any kind of splitting
2. Method should not be a hybrid formulation in terms of Lagrangian schemes.
Cheers
Aron
Positivity can be obtained using some standard limiter function on the numerical flux reconstruction. However, consider that the turbulence model is somehow a sort of limiting function. You can use an implicit formulation for the diffusive terms but if you add the turbulence term you need a linearization of the resulting system.
Aron Roland: Can you explain how you keep your method involving two time level only, if your treatment for diffusion terms is implicit? Is your convection term treated with first order accuracy?
Also, do you really take unstructured grid, all the way up to the solid body? I have noted that even for uniform flow past a circular cylinder, everyone uses structured symmetric grid near the cylinder surface. Otherwise, one will get non-zero lift for laminar flow! This has also remained a mystery to me about unstructured grid. How can one do adaptive mesh refinement near the boundary in such cases?
My personal approach (not sure where to put water depth in the overall context, as I don't solve for such variable):
1) I use a preconditioned, density based, coupled solver ( Article Implicit Solution of Preconditioned Navier-Stokes Equations ...
) with a Roe solver for the main equations, using a preconditioned HLLE scheme (Article Preconditioned HLLE Method for Flows at All Mach Numbers
) as entropy fix (so that it also ensures positivity, which is not ensured by the Roe scheme in near vacuum cases). Turbulence equations (and other scalars as well) are solved as segregated from the main equations. A dual time procedure is used to handle large CFL.2) I treat implicitly only the first order part of the fluxes and source terms. For source terms only, especially turbulent ones, I check that they do not decrease the diagonal dominance, and in case I just discard them. For turbulence models you can typically find specific ways to treat the source terms also in the original reference papers.
Gradients used to achieve second order for the convective scheme are also limited (several options: face-based/cell-based, standard/multidimensional, Barth&Jespersen/Venkatakrishnan). Gradients used to achieve second order for the diffusive fluxes are not limited (but some people limit them as well). Simple arithmetic average to compute face values from the adjacent cells.
3) Few sweeps of a block Symmetric-Gauss-Seidel or GMRES from PETSc.
4) Nothing fancy for the parallelization, I just use MPI with ghost cells and exchange things a couple of times (at the beginning of the iteration, for gradients and during the linear solve of the system) + few allreduce for monitoring stuff. This is how it works https://www.linkedin.com/feed/update/urn:li:activity:6408987249056317440
Hi Paolo, Tapan & Fillipo,
let me digest this and I will come back to u.
Cheers
Aron
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