# Simulating flow in a branched pipe

I am trying to simulate 1D advection and convection of a solute in the following blood vessel segment. I would like to know if this system can be simulated in COMSOL or MATLAB.

I have used pdepe solver in MATLAB for simulating flows in 1D pipes without branches. However, I am not aware of a tool that can be used for simulating simple branched segments like the above. Any suggestions?

• That's a question you should ask on the Comsol or Matlab mailing lists/forums. In essence, what you have here is a "quantum graph" on which you want to solve your system, and among the questions you'll have to answer is how flow decides which branch of the pipe to take. Nov 20, 2019 at 16:46
• @WolfgangBangerth Thanks a lot for the response. I'll post on both mailing lists. For, the toy model that I want to simulate, the velocity of the fluid in each segment of pipe is available. I am not aware of studies that have used "quantum graph" approach. Is this a commonly used approach for studying flow dynamics in pipe networks? Nov 20, 2019 at 17:21
• Well, a quantum graph is really just a network where you have an ODE or PDE on each edge. If you simulate each pipe segment via a 1d model, then in essence a pipe network is a quantum graph. Nov 21, 2019 at 4:41
• @WolfgangBangerth Thank you, I'm am trying to solve using a similar approach that you mentioned. But, it is not clear to me how flux conservation is established at a node connecting two edges. I also posted a question on this recently. If there are references in the literature that have implemented this kind of approach, I would be happy to learn from those implementations. Nov 21, 2019 at 5:10
• Flux conservation is simply an algebraic condition (not a differential equation) that has to hold at any given time: Whatever flows into a node at time $t$ has to flow out of it a time $t$. Nov 22, 2019 at 1:09