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Old   June 27, 2005, 22:26
Default Adaptive time step
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styoung317
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Hi,everyone! The following question confused me: In a dynamic process, we may set the time step according to Courant's condition to assure stability , |v*dt/dx|<1, in which v is the largest characteristic velocity; as the time ellapses, the velocity is changing ,too, so can we change the time step accordingly? Or some implicit principle exists? Thanks in advance. Young
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Old   June 28, 2005, 02:16
Default Re: Adaptive time step
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shekharc
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off course u can change time-step everytime.
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Old   June 28, 2005, 07:41
Default Re: Adaptive time step
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styoung317
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Thank you for response! Actually,I found that it was not feasible. For example,if a time step of 1e-5 is used, after an interval of 0.2s or so,the value of velocity will be one tenth of the initial one,but a corresponding time step of 1e-4 results in divergence.

My strategy of pressure correction may account for that,I think it somewhat affects the stability of calculation.
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Old   June 28, 2005, 09:46
Default Re: Adaptive time step
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shekharc
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u keep n eye on each component of the velocity throughout all the grids, evaluate u/dx, v/dy, and w/dz for all the grids. Now, say c = max(|u|/dx, |v|/dy, |w|/dz). So, u use dt = CFL/c.

For viscous flow calculations, there is more constrain u shud take into account...the Grid-Fourior number. dt < [dx*dx*dy*dy*dz*dz]/[2*KIN_VISC*(dx*dx + dy*dy + dz*dz)].

At last, your required dt would be the minimum of the two.

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Old   June 28, 2005, 15:13
Default Re: Adaptive time step
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ganesh
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Dear styoung317,

One way of solving dynamic problems or unsteady problems is to use the concept of pseudo-time stepping or Dual time stepping by which you introduce a dual step in addition to each physical step. At each physical time step, you will be trying to drive the pseudo-time derivative to zero, thereby solving a steady problem and then for this case you can use implicit time stepping and accelerate convergence. Of course in sucha case the physical time step is generally held constant to a vlue based on some physical considerations the problem possesses. Trying a fully explicit scheme is not wrong, but as you would have already seen, it would go too slow, for your time step will be restricted by physical considerations. Even for a steady case we compute the dt as you mentioned by the CFL criterion, using the largest eigen value, which again is a function of the solution and will change with iteration. Hope this helps.

Regards,

Ganesh
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