Stokes Flow with Pressure Inlet Conditions

Specific Domains Numerics
1

Are there examples of simulating (Navier-)Stokes flow by imposing pressure inlet conditions using VoronoiFVM, WaterLilly, Oceananigans, Trixi or similar?

Thx.

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2

This sounds like a problem you could solve with Gridap.jl

There are even tutorials on this:

  1. Navier-Stokes
  2. Stokes
2 Likes
3

I definitely agreed that the use of Gridap.jl is tempting here.

I do have examples similar to the ones you point to up and running.

It is the alternative implementation of the pressure boundary condition that I am wondering about.

Thx.

4

This is really tricky mathematically but in engineering practice It is an important condition for internal flows. This kind of BC is nonlinear in nature. Usually the implementation of this BC involves setting the total pressure on the inlet. Guess the static pressure and calculate the velocity. Compute the flow and get a better value for static pressure, compute inlet velocity again (you will need to specify flow direction!) and so on.

Check out this video: https://www.youtube.com/watch?v=Er2j5Kq17as

In some cases you can simplify the problem. As an example, take the DNS flow in a long pipe where you don’t want to bother with flow development. One possibility I’ve used before, is to set a periodic condition for the inlet and outlet. How do we specify the pressure? Use a body force to represent the mean pressure gradient.

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5

Precisely what I am looking for. Many thanks!

Any implementation in Julia?

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For my dissertation project, I implemented a boundary element method analysis of Stokes flow inside a rigid tube in MATLAB. If you’d like to take a look, the link is here.
I will, at some point, port this to Julia, but I cannot predict when that will be; hopefully, it will be soon.

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Congrats for your thesis! I have a lot of appreciation for people that make BEM codes work.

The tutorial Incompressible Navier-Stokes equations via DifferentialEquations.jl · Ferrite.jl employs BlockArrays to store the finite element pressure-velocity coupled matrix. I imagine that this format allows to form Schur complements and approximations thereof. First experiments with Schur complement preconditioning might therefore be easy to set up.