MATLAB: Can anybody help me understanding this mentioned line of code

acousticdigital image processinglaplacianmaskpropagationsound wavesultrasoundwavewave equation

Nx=100;
FldLngt=8e-3; 
DeltLngt=FldLngt/Nx;
--->PDz2(i,j)=(P(i-1,j-1)+P(i,j-1)+P(i+1,j-1)+P(i-1,j)+P(i+1,j)+P(i-1,j+1)+P(i,j+1)+P(i+1,j+1)-8*P(i,j))/(DeltLngt^2*2);<---
PDt2(i,j)=C(i,j)^2*PDz2(i,j);
where
Nx=grid points in x direction
FldLngt= length of simulation field
Delt is for Delta
PDz2= 2nd derivation of pressure with respect to z direction
PDt2=2nd derivation of pressure with respect to time t
I know that it is wave equation calculated using laplacian mask but i couldn't understand the denominator in mentioned line.

Best Answer

The numerator is the Laplacian under the assumption that there is unit distance spacing between adjacent grid points of the pressure array P. The ‘DeltLngt^2’ in the denominator corrects this so that it becomes the Laplacian assuming the actual distance values between adjacent grid points in both the x and y directions. I don’t know what the ‘2’ means in the denominator.
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