I'm doing a 2D transient simulation of turbulent flow past a sharp-edged rectangular bluff body. I'm using a version of k-omega model for turbulence modeling. My objective is the time-averaged flow field; I'm not interested in the instantaneous field. The problem is that I'm not sure how to choose an efficient timestep size.
In the literature, i have come across two methods in this regard:
(a) The timestep is adjusted repeatedly to ensure a max/rms Courant number, or
(b) based on an estimation of the Strouhal number (associated with the dominant frequency of vortex shedding) known from previous experiences, the timestep size is determined such as to resolve each vortex shedding cycle through n temporal increments.
The problem is that, i couldn't find any consensus in the literature over appropriate values for max/rms Courant number or n in either methods. I understand that this should be really addressed through a sensitivity study, but I have very limited computational power to afford that, especially given that it takes a long time for the simulations to reach a statistically converged solution. I am hoping there's some reliable rule of thumb or related studies to use, thereby avoiding such a sensitivity analysis.
I would appreciate your comments.
A true time accurate solution is obtained by keeping the Courant number below 1. The explicit time integration methods requires this condition to be true for stability and accuracy. One benefit is that you don't need to solve a large linear system of equations, but 1 iteration per time step is sufficient..
Some techniques such as transient SIMPLE, SIMPLEC (or fully coupled solvers/ dual time integration) ... can be used with a larger time step, even CFL = 20, 100 etc... but you will need to put enough inner iterations in each time step to reduce the residuals to near zero values for that particular time step..
Now the question is how to choose a time step..? At high Reynolds numbers and for aerodynamic flows this becomes a problem due to having large stretched cells in the boundary layer... So if you were to go with CFL < 1 the simulation becomes very expensive.. For implicit systems with some iterations per time step can be effectively used with time step estimates based on the Convective time scale, I have seen papers where people have used 0.01 to 0.1 of c/U. Another approach is to put at least 50-100 time steps in each oscillation of the vortex shedding time period.. This way you will filter out the high frequency oscillations (which I believe you are not interested in)...
Hope this helps..
Best
Hi Armin
I suggest you find some high-quality articles in the field and assess their relevant time steps considered. I think it ensures your simulations and recognizes the limitations regarding the time step.
Best,
Choosing an appropriate timestep size for transient simulations can be challenging and typically requires some degree of trial and error. While there is no universal rule of thumb, there are some guidelines you can follow to make an initial estimate of the timestep size.
The max Courant number and n increments method are commonly used in the literature to estimate the timestep size. However, the appropriate values of these parameters can vary depending on the specific problem being simulated.
A general guideline for choosing the maximum Courant number is to keep it below 1.0, but this can vary depending on the simulation. A lower Courant number will result in a more accurate solution but will also increase the computational cost. A higher Courant number can reduce the computational cost but may result in numerical instabilities and inaccurate results.
For the n increment method, the timestep size is chosen to ensure that each vortex shedding cycle is resolved by n temporal increments. The appropriate value of n depends on the dominant frequency of vortex shedding and the timescale of the problem. In general, a higher value of n will result in a more accurate solution but will also increase the computational cost.
Since you have limited computational resources, a reasonable starting point would be to use a maximum Courant number of 0.5 and a value of n that is equal to the dominant frequency of vortex shedding divided by the total simulation time. This is a conservative estimate that should ensure stability and convergence, although it may result in a longer simulation time.
It is also important to ensure that the timestep size is small enough to resolve the smallest turbulent scales in the flow. A general guideline is to choose a timestep size that is less than 10% of the smallest turbulent timescale in the flow.
In summary, while there is no universal rule of thumb for choosing an appropriate timestep size, a maximum Courant number of 0.5 and a value of n equal to the dominant frequency of vortex shedding divided by the total simulation time are reasonable starting points that should ensure stability and convergence. It is also important to ensure that the timestep size is small enough to resolve the smallest turbulent scales in the flow.
- Badges
- Science topic
- Similar topics
- Mathematics