# Sound Propagation using Finite-Difference Time-Domain (FDTD) considering wind effects

I am trying to plot the propagation of sound from a fixed source in a 2D environment using Finite-Difference Time-Domain (FDTD) Method taking into account the effects of the wind velocity. I came across the following set of equations for solving the equation for pressure with respect to time at different grid points in the 2-D environment.

$$\frac{∂p}{∂t} = -( v_x\frac{∂}{∂x}+v_y\frac{∂}{∂y})p - \kappa(\frac{∂w_x}{∂x}+\frac{∂w_y}{∂y}) +\kappa Q$$ $$\frac{∂w_x}{∂t} = -(w_x\frac{∂}{∂x}+w_y\frac{∂}{∂y})v_x- (v_x\frac{∂}{∂x}+v_y\frac{∂}{∂y})w_x-b\frac{∂p}{∂x}+bF_x$$ $$\frac{∂w_y}{∂t} = -(w_x\frac{∂}{∂x}+w_y\frac{∂}{∂y})v_y- (v_x\frac{∂}{∂x}+v_y\frac{∂}{∂y})w_y-b\frac{∂p}{∂y}+bF_y$$ where, $b = \frac{1}{\rho}$ is the mass bouyancy.

But, I am unable to figure out what $\vec{F}$ and $Q$ are? They are mentioned somewhere as dipole and monopole pressure sources respectively. What does they actually mean?

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A monopole pressure source is one that radiates the pressure source in all directions. That is why it is a source term directly on the pressure term -- it is "injecting" pressure at a point. Think of dropping a pebble in the water, the waves that ripple outwards are a monopole source.

The dipole pressure source terms are ones that do not radiate equally but sort of oscillate back and forth. A piston moving is a good example -- on the leading edge, it generates high pressure while on the trailing edge, it generates low pressure.

A simple search for "monopole pressure source" turned up the following site in the top few results that shows animations for monopole, dipole and quadrupole sources as well as descriptions that make it clear:

Can you guide me how can I calculate $\vec{F}$ and $Q$ in the above equation? –  Divanshu Jun 27 '13 at 13:29