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 January 29, 2008, 09:14 Adaptive time stepping #1 Simon Guest   Posts: n/a What is adaptive time stepping. what are advantages and disadvantages of it in the context of large eddy simulation. Thank you very much in advance for your reply. With regards Simon

 January 29, 2008, 10:48 Re: Adaptive time stepping #2 Patrick Guest   Posts: n/a The time step is never taken to be constant as far as I know it is always "adaped" to the velocity, grid size and viscosity (or even radiation). For a sound velocity c and flow velocity v (say in one dimension x), then the CFL (Courant Friedrich Levy) condition is delta x / delta t > (c+v) where delta x is the grid spacing and delta t is the time step, such that the velocity of the numerical integration delta x/ delta t is larger than the velocity in the fluid equations (so that it can follows the flow/evolution of the flow). THis gives delta t < (delta x) / (c+v) If it is a viscous flow with mu = rho * nu then delta t < (delta x)^2 / nu A similar restriction applies for a radiative term taken in the diffusion approximation, etc... So each time step the size of the time step is adapted to the grid size, velocity of the fluid and sound and value of the viscosity nu = mu/rho

 January 29, 2008, 11:10 Re: Adaptive time stepping #3 Mani Guest   Posts: n/a Hi patrick thanks for your reply. You didnt tell me about its advantages and disadvantages particularly in the context of LES. If you can direct me to some material that will also be very useful. Help documentations have virtually nothing. Thank you

 January 29, 2008, 11:45 Re: Adaptive time stepping #5 Chris Guest   Posts: n/a Hi Patrick You have cleared some of my doubts regarding time-stepping. Thanks for that! My code uses fully implicit scheme. I guess most of the things that you have said will have no relevance to time-implicit code. I am just confused how should i choose my time step for an implicit code. Its quite simple for an explicit code because one needs to keep courant number below 1. However, for an implict code courant has no relevance what so ever. Thats why i wanted to use adaptive time stepping. How would you choose your time step for LES simulation. Thank you very much

 January 29, 2008, 11:54 Re: Adaptive time stepping #6 Patrick Guest   Posts: n/a IN the implicit case the restriction on the time step comes from restriction on the size of the elements of the matrix you have to invert. If the viscous term only is taken implicitly then you still need the CFD condition for the explicit terms. You also need to check the conservation of energy and momenta as a function of the size of the time step as part of the errors. Usually also one uses only a fraction (say 0.5) of the "theoretical" time step. Here this needs to be first tested with the code and the problem to decide how large this fraction can be.

 January 29, 2008, 11:56 Re: Adaptive time stepping #7 Chris Guest   Posts: n/a Thank you patrick. Chris

 February 7, 2008, 00:15 Re: Adaptive time stepping #8 agg Guest   Posts: n/a Hello Chris, One point I would like to add for implicit time stepping. Using an implicit time step, you may be able to use a larger time step as compared to an explicit scheme. This is just a numerical artifact. When you want to capture certain physics in the flow, such as vortex structures, you might want to tune your time step, so as to be able to actually visualize small structures. If your time step is larger than the time scale of certain structures, you will never see them ! Sometimes we capture things when we least expect them - serendipity

 February 7, 2008, 07:23 Re: Adaptive time stepping #9 Chris Guest   Posts: n/a How can one tune time step during a simulation? Thank you for your answer. It was helpful!

 February 7, 2008, 12:41 Re: Adaptive time stepping #10 agg Guest   Posts: n/a Well, based on intuition. You are trying to capture structures. Maybe you have experimental data that can give you an estimate of time scales for such structures. Even if you don't, you can try to guesstimate.

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