Transient Simulation of Oscillating Pressure Waves
I am attempting to model Womersley Flow in a circular pipe.
What boundary conditions should I use? At the moment I am setting one entrance side of the pipe as an "opening" with static pressure entrained, prescribing the pressure as a cosine function in time (oscillates between amplitude of a cosine wave) with a frequency of 3Hz. The other side of the pipe is set as an "opening" with static pressure entrained as 0 for all times. The walls of the pipe are set to no slip. the initial conditions are set as zero velocity and pressure, and the dynamic viscosity of the fluid is modified to allow simulation of various womersley numbers. Total time is set to 2secs, with time steps at 0.001 steps. The B.C at the entrance opening is applied at every time step (i.e. at every time step a new B.C is given according to function Pressure=A*cos(6*pi*t) ). However I do not get the trademark Womersley velocity profile  instead I get something resembling a plug flow. Any thoughts on why this might be the case? Could it be that solution hasn't converged? I use 2nd order euler with 5 coefficients. Or is it that the time steps need to be more frequent than the oscilating B.C's? at the moment, every time step has a different BC. 
You should do a sensitivity analysis on mesh size, convergence tolerance and timestep size. Only when you have established all these parameters are OK do you have any hope of an accurate result.

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