I am doing focused ultrasound simulations in 2D. Could you explain to me what you do in the third dimension is this case? Do you set the pressure to zero in the third dimension?

From the manual it is clear that the input source.p0 has to be put in the units N/m^2 (independent of the amount of dimensions). By conversion the source term Ms is found using Equation 2.19. In this equation the parameter N is used to describe the amount of dimensions. What is the reason for the use of this parameter N?

When looking at a point source in 2D the intensity decreases with distance according to: I = P0/(2pi*x), with P0 the input power in Watt and x the distance from the point source in meters. Using that I = p*v = p^2/(rho*c0) it is found that: p = sqrt(P0*rho*c0/(2pi*x)). When looking at the units of this pressure, it is not in N/m^2. When doing the same derivation of the pressure in 3D you actually do get the correct units, since then I_3D = P0/(4pi*x^2). So I am wondering if this mismatch in units here is also something which is accounted for in the k-wave simulation? And is so, how is this done precisely?

Thanks in advance!