It is difficult to say if the analytical or numerical impedance solutions are better. Each has its strengths and weaknesses and may be useful depending on the problem of interest. The analytical solution has a smaller computational expense than the numerical solution. On the other hand, the analytical solution also relies on simplifications, such as the use of average fluid properties, a one-dimensional coordinate system, and a uniform flow field. The numerical simulation does not rely on these simplifications, but it does depend on mesh discretization, as discussed in the previous paragraph. At the end of the day, the numerical and analytical solutions both give estimates of impedance; while we do not know which is better, we assume they represent a reasonable range.