k-Wave

1. huangchao
   

   Member
   Joined: Nov '10
   Posts: 57

   Hi Dr. Cox and Dr. Treeby,

   I am trying to use the kspaceFirstOrder3D function to simulate wave propagation in media with varying sound speed and with a time varying pressure source term s(r,t) and zero initial conditions. So I wonder using kspaceFirstOrder3D is equivalent to solve which of the following 2nd order wave equations:

   1. (∂^2/∂t^2 - c(r)^2∇^2)p(r,t) = s(r,t) subjects to p(r,0)=0, ∂p/∂t|t=0 = 0;

   2. (∇^2 - 1/c(r)^2∂^2/∂t^2)p(r,t) = -s(r,t) subjects to p(r,0)=0, ∂p/∂t|t=0 = 0;

   Also, are the following settings for the input structure source correct for my case?
   source.p0=0;
   source.p=s;
   source.p_mask=s_mask;
   source.p_mode='additive';

   Thanks a lot for your time and Happy New Year!

   Best,
   Chao

   Posted 11 years ago #

2. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Chao,

   Probably quickest if you have a look in the k-Wave manual (under documentation). I think Section 2.3 (and surrounding sections) answers your question. If not, please post again.

   Happy New Year too!

   Ben

   Posted 11 years ago #

3. huangchao
   

   Member
   Joined: Nov '10
   Posts: 57

   Hi Dr. Cox,

   Actually, I am trying to use the kspaceFirstOrder3D function to simulate the wave propagation governed by the wave equation (∇^2 - 1/c(r)^2∂^2/∂t^2)p(r,t) = -s(r,t) subjecting to p(r,0)=0, ∂p/∂t|t=0 = 0, where the source term s(r,t) is given and it's obviously not in the unit of pressure, although I called it pressure source in the original post.

   After studying the k-Wave user manual, I found that the above s(r,t) is corresponding to ∂S_M/∂t in Eq. (2.9) provided there is no velocity soureces. Also, in k-Wave, the source.p is scaled to be unit of S_M so that it can be added in the equation of mass conservation.

   So to simulate the above inhomogeneous wave equation in my case, I need to integrate s(r,t) first and set the integral values to source.p, then comment the line kspaceFirstOrder_scaleSourceTerms, after that the simulation results from kspaceFirstOrder3D should be consistent to the above wave equation. Is this right?

   Thanks,
   Chao

   Posted 11 years ago #

4. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Chao,

   kspaceFirstOrder_scaleSourceTerms takes into account the fact that you are inputting the source over a finite region, a voxel, and a finite time, dt.

   To check your simulation is set up to give you the same units out that you put in, turn off the absorption and propagate a plane wave which won't spread geometrically. You may want to turn off the PML at the edges perpendicular to the wave so it is truly modelled as 1D.

   Kind regards,

   Ben

   Posted 11 years ago #

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