k-Wave

1. huangchao
   

   Member
   Joined: Nov '10
   Posts: 57

   Hi, Dr. Cox and Dr. Treeby,

   I found that the condition for prompting the warning "time step may be too large for a stable simulation" is:

   dt > DT_WARNING_CFL*max([kgrid.dz, kgrid.dx, kgrid.dy])/max(medium.sound_speed(:))

   But in my opinion, "min([kgrid.dz, kgrid.dx, kgrid.dy])" should be used instead of "max([kgrid.dz, kgrid.dx, kgrid.dy])", because for a fixed "DT_WARNING_CFL", "dt" should be less than "DT_WARNING_CFL*min([kgrid.dz, kgrid.dx, kgrid.dy])/max(medium.sound_speed(:))". I don't know if this is right?

   Another thing I want to make sure is that if the simulation is stable as long as "DT_WARNING_CFL<1".

   Thank you very much!

   Best,
   Chao

   Posted 12 years ago #

2. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,643

   Hi Chao,

   The check is really just to make sure that if people have manually defined kgrid.t_array (rather than using makeTime), that the time step is within a sensible range. You are right that if the grid spacing happens to be anisotropic, taking the minimum will give a more stringent warning. However, simply replacing max with min won't work in this case because kgrid.dz is zero in 2D and kgrid.dy and kgrid.dz are zero in 1D.

   A good discussion on the CFL condition required for stability (at least in the case of a heterogeneous sound speed) is given in the paper by Mast et al. (2001) "A k-space method for large-scale models of wave propagation in tissue". It depends on both the maximum sound speed in the medium, and the scalar sound speed used inside the k-space operator.

   I hope that helps,

   Brad.

   Posted 12 years ago #

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