Solution won't stabilize

[Vitaly Kheyfets]

Hello -

We are having issues getting a periodic solution. When we tried the simulation with our own code, the solution reached a periodic waveform within 3 cycles. However, SimVasc appears to need up to 7 or 8 cycles (the attached image shows the first 4 cycles of increasing pressure).

This seems like an initial condition issue, but I'm surprised that our own code didn't have the same problem.

Thank You,

Vitaly

[Weiguang Yang]

Is this pressure an outlet pressure with an RCR boundary condition? If so, it is likely that the gradual increase in pressure is caused by a relatively large RC constant. If I remember correctly, the RCR analytical solution includes a term for initial conditions, which decays as exp(-t/(C*Rd)). If C*Rd is small, the influence of initial values disappears quickly and the solution reaches a stable periodic state in a couple of cycles. You can verify how many cycles it takes to become stable for given RCR values by plugging periodic flow to an RCR circuit model.

[Vitaly Kheyfets]

Thank You for your response. This pressure is the inlet pressure (we are applying flow as the inlet BC), but we are using an RCR outflow boundary condition. If I plug our flow directly into an RCR circuit (with the same RCR values), we see convergence in 2 cycles.

This is a good point though. It never occurred to me to think about the outflow BC. I kept focusing on the initial values within the domain. Although, if it is the BCs, I am not sure what can be done about that.

I really appreciate any suggestions!

Best,

Vitaly