Implementing equation with two unknowns

test1 · February 22, 2021, 04:30

Hi,

I´m struggling with the implementation of an equation into my own OpenFoam-Solver.
I´ve got two equations like this:
ddt(X) + div(n1) = -Q
ddt(Y) + div(n2) = Q

X, Y and Q are unknowks; n1 and n2 are knows.

To avoid the calculation of Q I would like to equalize the equations

ddt(X) + ddt(Y) + div(n1) + div (n2) = 0

this gives me an equation with the two unknows X and Y.

Now I would like to solve this equation by inserting a value for X, calculate Y and repeate this procedure till I have a result of this equation.

Is there a way to do something like this in OpenFoam?
Actual I have no Idea how to type in an equation with two unknows and I´m not sure if this plan is a good idea, because I think this could result in an instable solver.

I will be glad, if you have some tips for me.

Tobermory · February 22, 2021, 07:45

I think that you have a problem here - you have 2 equations and 3 unknowns ... or 1 equation and 2 unknowns if you get rid of Q. You can't solve this! You need another equation.

You can solve Y for a given value of X, or vice versa, but there is no single solution of X and Y given just one equation.

Tobermory · February 22, 2021, 08:35

gionni · February 22, 2021, 12:08

Quote:

Originally Posted by test1

Now I would like to solve this equation by inserting a value for X, calculate Y and repeate this procedure till I have a result of this equation.

What you are saying is that you would like to solve iteratively the system, or the equation in x and y. To do so, you give a value of x and you get a value of y; when do you consider yourself satisfied? Basically you need a relation for x and y that determines that that solution is ok. So that's your 3rd equation.
Find the criterion, write it as an equation and you can close the system.

Hope it helps!

test1 · February 23, 2021, 01:34

Thanks Tobermory and gionni,

I´m going to look for the relation of X and Y to close the system.
Your completely right that I need the third equation to make sure that the pair of X and Y are the correct pair that I need.

Thanks for your help and the food of thought.

February 22, 2021, 04:30	Implementing equation with two unknowns	#1
test1 New Member anonymous Join Date: Dec 2018 Posts: 4 Rep Power: 7	Hi, I´m struggling with the implementation of an equation into my own OpenFoam-Solver. I´ve got two equations like this: ddt(X) + div(n1) = -Q ddt(Y) + div(n2) = Q X, Y and Q are unknowks; n1 and n2 are knows. To avoid the calculation of Q I would like to equalize the equations ddt(X) + ddt(Y) + div(n1) + div (n2) = 0 this gives me an equation with the two unknows X and Y. Now I would like to solve this equation by inserting a value for X, calculate Y and repeate this procedure till I have a result of this equation. Is there a way to do something like this in OpenFoam? Actual I have no Idea how to type in an equation with two unknows and I´m not sure if this plan is a good idea, because I think this could result in an instable solver. I will be glad, if you have some tips for me.

February 22, 2021, 08:35		#3
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 670 Rep Power: 14	<for some reason the same message posted twice ... can't delete this duplicate one> Last edited by Tobermory; February 23, 2021 at 04:06.

February 23, 2021, 01:34		#5
test1 New Member anonymous Join Date: Dec 2018 Posts: 4 Rep Power: 7	Thanks Tobermory and gionni, I´m going to look for the relation of X and Y to close the system. Your completely right that I need the third equation to make sure that the pair of X and Y are the correct pair that I need. Thanks for your help and the food of thought. Tobermory likes this.

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February 22, 2021, 07:45		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 670 Rep Power: 14	I think that you have a problem here - you have 2 equations and 3 unknowns ... or 1 equation and 2 unknowns if you get rid of Q. You can't solve this! You need another equation. You can solve Y for a given value of X, or vice versa, but there is no single solution of X and Y given just one equation.