# Interesting results of an incompressible flow with only no-slip boundary in a bounded domain

Hey dear users

Background: Imagine we have the time-dependent incompressible Navier-Stokes equations with an initial condition and no-slip (homogeneous Dirichlet boundary) on the whole boundary, i.e.

\begin{aligned} \partial_t u - \nu \Delta u+(u \cdot \nabla)u+\nabla p = f \\ \text{div} u=0 \\ u(x,0)=u_0(x) \text{ on } \Omega \\ u=0 \text{ on } (0,T)\times \partial\Omega\end{aligned}

As the space domain Iād like to take a bounded Lipschitz domain (e.g. C^1 boundary), so I just took a ball as my first test. And this ball is filled with some fluid - e.g. water. Further I want to take an initial condition that is quadratically integrable, i.e. u(x,0)=u_0(x) on \Omega and u_0 \in L^2(\Omega). And a outer force f \in L^2((0,T) \times \Omega) in the Navier-Stokes equations.

What I want to do: I wanted to have some āniceā and āinterestingā results that happen inside the ball. Some rotation or some sorts. This is not that easy for me to achive with only using no-slip boundary and no inlets/outlets Of course, taking an uniform initial condition just leads to a uniform result.

Do you have some ideas what I could do to get a nice result?

I thought of taking an initial condition that gets me some rotation. But I could only take uniform initial conditions with SimScale and I had some problems with the āRotating Zonesā and āSolid Body Motionā options in this specific case. Could you maybe tell me what I should do in these options?

The project is the following: https://www.simscale.com/workbench?publiclink=9235df82-c3d8-4583-b8e8-a1d5e0fb9ea3
I just imported a ball and generated a mesh, nothing much.

Thank you so much,
Marvin

Hi Marvin (@mfritz)!

I will have a look at your project later on. In the meantime I am tagging my colleagues @sjoshi and @gholami here. They might give us some interesting information about your project.

Cheers,

Jousef

2 Likes

Hi Marvin,

Based on my understanding of the problem, youāll need a variable initial condition which is unfortunately not yet available on SimScale (although it is in OpenFOAM). Letās wait and see if anyone else has a work around for this

Cheers,
Anna

1 Like

Hi Marvin (@mfritz)!

Coming back to your initial post.

Are you sure that your initial conditions lead to the same result everytime? I do not think that is the case as the flow behaviour always changes even with the same initial conditions.

For your project idea, you could have a look at this project from my colleagure @Ali_Arafat: Sloshing of Fluid in a Moving Fuel-Tank

There you will see that a Solid Body Motion has been used with an Oscillating linear motion.