Dear colleagues, I am performing DNS with the Burger equation (1D) without force and with periodic boundary conditions. So, the initial condition (the energy content) will decay towards zero due to the viscous forces. In other words, the viscous force will consume all the energy introduced by the initial conditions. Thus, I will never get a steady state solution where statistics can be computed. Specifically the mean of the velocity. Since I need to compute the turbulent kinetic energy and its dissipation (kappa and epsilon) I need to compute the fluctuating velocity but to do so I need the mean of the velocity. How can I compute the mean of the velocity from a data set that never reaches a stationary condition
Dear Xavier, thank you very much for your reply and your kindness sharing your work with me. Indeed, it is very difficult to quantify the role of the forcing term. Because you do not know beforehand if this force will balance the inertial/viscous force. Also, if you want to filter the equation, and thus the force, how will you filter the force. This is an endless discussion. However, I have seen papers without force, but they always end-up adding the force too, due to the higher fluctuation that is achieved with the force. Unfortunately I do not speck french but math is universal and I have a very good friend who does "Google Translator".
Xavier I forgot to ask you about the information you uploaded. Did you used pseudo-spectral methods right? This is something has giving me a lot of trouble because I am representing the derivatives by finite difference and not by expansion of harmonics functions. Thus it has been very difficult to find information about how to define the random force. Also, I saw you introduce the force only at the wave number k=2 and k=3 which I have no clue how to do it in physical space. Why did you choose white noise and not a Gaussian random force?
Your calculation should be instantaneous. A photograph of the flow each time. For every time you have a field of the velocity then the calculation is easy only for this time. You can observe the evolution of the statistics not only for k and epsilon but also for mean velocity. To see the fluctuation you have to calculate the mean velocity unless locally (spatial or temporal). The spatial statistics is not the same as temporal statistics.
Dear Xavier, Thank you very much for your reply. Yesterday I was computing the spectrum Energy of my initial condition but It does not look good at all. I think the issue is with the initial condition that may be causing this problems. If you take a look the tails of the spectrum (at the highest wave number) the slope tends to increase and is not even capturing the "trend" of the viscous dissipation. Xavier How did you initialize your velocity field U(x,0). By the way, I lived in Germany when I was 17 I have forgotten all my German even though It was like my second tongue. And I went to the DLR that placer is AWESOME.!!!
Professor: Granados, I appreciate your reply too. I am glad that people from my home and lovely country are working in this field, well that is why "La Simon Bolivar" is one of the best in Venezuela. I found the solutiuon at Pope's Book and Also at Davidos text book. Owever, I invite you to comment about my issue with the energy spectrum..
Dear Xavier, I agree with you with the fact that the Initial spectrum energy is not that relevant. However, it is important to show important features of the initial condition.
According to your explanation you computed the average in time of the energy spectrum. So I guess, you computed several energy spectrum and then you performed an "ensemble average" with them. Is it right?. My case is different because I have a freely decay turbulence, so the time average is not the right path. However, the concept is the same with the space average.
I Lived in Mechernich, I went to Koln to visit the DLR. was AWESOME. I loved Germany and I hope to go back, someday!!!...
Finally Xavier, I want TO THANK YOU FOR your kindness sharing with the me the information. I also, would like to show my code for the Energy Spectrum, I want to double check that it is right, because the energy spectrum I am getting is odd...
I saw your spectrum and they were all right. Please let me know if you do not mind take a look at my codes.. This is a very short one few lines
Julio please give me a complete reference for Davidos text book. The recommendations of Xavier sound good. Review my book chapter XV and appendix E section 5
https://www.academia.edu/11942882/Mec%C3%A1nica_y_Termodin%C3%A1mica_de_Sistemas_Materiales_Continuos
I couldn't see Pope book solution, not under Burgers equation.
- Badges
- Science topic