k-Wave

1. weigler
   

   Member
   Joined: Nov '16
   Posts: 3

   Hi all,

   first of all: I really like this toolbox and its handling!

   I got a question regarding my (very basic) 2D simulation of a wave propagating in air.
   I'm using a single-point-source and one sensor in a grid with constant length (m).
   Now my problem: If I increase the number of gridpoints while decreasing the gridspacing (i.e. maintaining the physical distance between source and sensor) I observe a significant decrease in the pressure recorded by the sensor. The signal-frequency used is well below the one supported by the grid.
   What am I doing wrong?

   Thanks in advance,
   Tobias

   Posted 8 years ago #

2. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Tobias,

   If, as well as recording the data at your sensor position, you also record it at the source position, you will see that the ratio of the two remains constant. k-Wave is correctly modelling the propagation, but what is happening is that the amplitude at the source is dependent on the grid spacing. One part of the reason is that you are using an 'additive' source, ie. successive values in the time-varying source are added to the value at the source grid point, rather than replacing them.

   The reason why this leads to a different amplitude is related to the underlying interpolation that k-Wave implicitly assumes to fill in between the grid points. It is inherent to the pseudospectral method k-Wave is based on. Consider a source defined at a single grid point. k-Wave has a representation of the source that matches at that grid point but is not zero everywhere else. Rather, it is a sinc function (strictly a periodic sum of sinc functions) whose zeros line up with all the grid points but which oscillates in between them. In other words, when we think we are adding a source at just one point, we are really adding a distributed source, whose amplitude drops from the value at the source grid point to zero at the neighbouring grid points. If the source consisted of just one value in time, then after a time of t = dx/c, there will not be much amplitude left at the source point: that main lobe of the sinc function will have propagated away by then. However, if, before that happens, additional source values (at time point 2, 3, etc) are added to the value at the source grid point then it will grow in amplitude. The actual amplitude that a long-duration additive source has will depend, therefore, on the grid spacing.

   One way around this issue is to set a 'Dirichlet' type source, which replaces the current value at the source grid point, rather than adding to it. The only thing to be aware of in that case is that, if there are waves coming back towards the source point, it will act as a scatterer.

   I hope that wasn't too confusing an explanation!

   Kind regards,
   Ben

   Posted 8 years ago #

3. weigler
   

   Member
   Joined: Nov '16
   Posts: 3

   Hi Ben,

   many thanks for your detailed answer! It wasn't confusing at all.

   Placing a sensor at my source position and setting the 'dirichlet' condition was the first thing I did before asking for advice.
   In my opinion the mistake I made was placing the Sensor directly ontop of the source and using just one starting pressure value.

   By moving the sensor a few gridpoints away from the source I finally got reasonable results.

   Many Thanks and best regards
   Tobias

   Posted 8 years ago #

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