dzabakh Posted March 27, 2017 Share Posted March 27, 2017 Hello everybody!I am trying to solve the wave equation in 3D[latex]\frac{\partial^2 p}{\partial t^2} - c^2 \Delta p = \delta(\vec{r}-\vec{r_0}) \delta(t-t_0),[/latex]where [latex]\vec{r_0}[/latex] is the radius-vector of the point source and [latex]t_0[/latex] is the moment when the source radiates a pulse, with Dirichlet boundary conditions.I am solving the equation with finite-difference method in time domain. The steps by time are done by Runge-Kutta 4. The source is put into one node and the time profile of the source is step-like. I made it step-like (see Pic. 1)because a point source should radiate a time-derivative of the incoming signal[latex]p(\vec{r},t) = \frac{\rho_0 S}{4\pi r} \frac{dv}{dt}(t-r/c_0)[/latex]and I want to get a delta-like signal from my source.When I solve the equation, what I get is an impulse on the receiver, see Pic. 2.This impulse is o'k but the amplitudes of such impulses fade incorrectly with distance. As I understand, it should be [latex]\sim 1/r[/latex] but in fact the amplitudes fade [latex]\sim e^{-\alpha r}[/latex], see Pic. 3. I think I have stated the source incorrectly. Maybe someone knows how to do it right? What can also be a reason? Is this some kind of grid dispersion?Thank you in advance. Link to comment Share on other sites More sharing options...
Klaynos Posted March 27, 2017 Share Posted March 27, 2017 What are your boundary conditions? Can you clarify that on the x axis it is distance from source at a given time? Link to comment Share on other sites More sharing options...
dzabakh Posted March 27, 2017 Author Share Posted March 27, 2017 What are your boundary conditions? Can you clarify that on the x axis it is distance from source at a given time? I have Dirichlet boundary conditions. Yes, the x axis is c*t, where c is the speed of sound and t is the time. Link to comment Share on other sites More sharing options...
Klaynos Posted March 27, 2017 Share Posted March 27, 2017 And the y axis is something like E^2? I'm not sure that you want dirchlet boundaries for your box. As that might give some unusual effects. I was expecting PMLs or similar. It has been 5 years... Link to comment Share on other sites More sharing options...
dzabakh Posted March 27, 2017 Author Share Posted March 27, 2017 And the y axis is something like E^2? I'm not sure that you want dirchlet boundaries for your box. As that might give some unusual effects. I was expecting PMLs or similar. It has been 5 years... Well, I cut the unusual effects off by a time window. I just want to send a pulse and the receive a diffracted pulse, I'm not much interested in the boundary conditions. Link to comment Share on other sites More sharing options...
Klaynos Posted March 27, 2017 Share Posted March 27, 2017 But if your boundary conditions are forcing a field value the. They will alter what you measure inside the box. What package are you using? It was a few years ago but i found meep very accessible. Link to comment Share on other sites More sharing options...
dzabakh Posted March 27, 2017 Author Share Posted March 27, 2017 But if your boundary conditions are forcing a field value the. They will alter what you measure inside the box. What package are you using? It was a few years ago but i found meep very accessible. My code is written in Matlab. No, I think the boundary conditions shouldn't affect the impulse coming straightly from the source to the receiver. This pulse doesn't know nothing about the boundaries. I cut off the other pulses reflected from the boundaries with time window. Link to comment Share on other sites More sharing options...
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