[Maxxxx]

Hey,


I´m new to OpenFoam and would like to implement a nonlinear equation to my solver.


Target Equation: C1 * (C2 + C3 * (C4 * |X0-X|)^0.1) * (X-X0) = 0



Where C1,C2,C3 are constant dimensionedScalars,
X0 is my fixed reference volVectorField and

X is the volVectorField I would like to calculate for each cell


As you can see, I do not have any derivative to use fvm namespace or something else.


Hence, following code does obviously not work:

fvVectorMatrix XEqn
(
     C1 * (C2 + C3 * (C4 * |X0-X|)^0.1) * (X-X0)
);
XEqn.solve();

Now my question: How can I solve equations like this with no derivative for each single cell. Is this possible? If yes are there multiple methods?


Help is appreciated


Max

[dlahaye]

How is X coupled accross various cells?

Does a loop over cells and a Newton-type iteration in each cell suffice?

[Maxxxx]

Hey,


and thank you for the answer.


My X0 is coupled over the whole mesh. What I would like to do is calculating my X without any coupling meaning I can also calculate it for each cell with a loop as you said, but how?


Tanks you


Max

[dlahaye]

You can put a root finding algorithm inside a loop over cells.

To implement loop over cells, see e.g.

https://github.com/UnnamedMoose/Basi...mmingTutorials

A root finding algorithm can be found inside the boost libraries, see e.g. https://www.boost.org/doc/libs/1_64_...kit/roots.html. OpenFoam builds upon boost. Possible you can try to develop a boost solver outside of OpenFoam.

[@ss]

I want to use non-linear spring stiffness to solve motion equations in openFoam. can anyone tell me how I can do that?

[alundilong]

please elaborate your question,
provide background and formula of interest would definitely help.

[alundilong]

Originally Posted by @ss

I want to use non-linear spring stiffness to solve motion equations in openFoam. can anyone tell me how I can do that?

please elaborate your question,
provide background and formula of interest would definitely help.

[@ss]

First of all, Thank you sir for your response.....
sir, I am working on energy harvesting from vortex-induced vibration in which I use non-linear spring stiffness instead of linear stiffness in the spring mass damper system using OpenFOAM software.

my ̈ + Cy ̇ + ky +by^3= Fy

I am not able to introduce nonlinearity in the motion equation in openFoam and also I am not able to find any video or tutorials related to this.
I have done simulations with linear systems for isolated and multi-body but have not been able to do with non-linear systems.

[alundilong]

Originally Posted by @ss

First of all, Thank you sir for your response.....
sir, I am working on energy harvesting from vortex-induced vibration in which I use non-linear spring stiffness instead of linear stiffness in the spring mass damper system using OpenFOAM software.

my ̈ + Cy ̇ + ky +by^3= Fy

I am not able to introduce nonlinearity in the motion equation in openFoam and also I am not able to find any video or tutorials related to this.
I have done simulations with linear systems for isolated and multi-body but have not been able to do with non-linear systems.

You might borrow the ODEsystem and ODESolver to find solution of this second order ODE. Please see the attached file to further explanation.