CODEWITHSUNDEEP
modelica
prasadshet
prasadshet

Reputation: 96

how to use Partial derivative in modelica?

If i have to use a partial derivative in modelica, how can that be used. I am not sure if partial derivative can be solved in modelica but i would like to know, if it can be used then, how should it be implemented.

Upvotes: 1

Views: 1966

Answers (2)

Samir Khan
Samir Khan

Reputation: 11

I've discretized PDE systems for solution in Modelica: heat equation, wave equation, PDEs from double-pipe heat exchangers, PDEs from water hammer to model pressure surges in pipelines etc

At a simple level, you can replace the spatial derivative with a central difference approximation, and then generate the entire set of ODEs with a for loop. For example. here's a Modelica code snippet for a simple discretization of the heat equation.

parameter Real L = 1 "Length";
parameter Integer n = 50 "Number of sections";
parameter Real alpha = 1;
Real dL = L/n "Section length";
Real[n] u(each start = 0);

equations
u[1] = 273;  //boundary condition
u[n] =0;   //boundary condition

for i in 2:n-1 loop
  der(u[i]) = alpha * (u[i+1] - 2 * u[i] + u[i-1]) / dL^2;
end for;

This is just a simple example entered from the top of my head, so excuse any mistakes.

Do you have a specific example or application?

Upvotes: 1

Michael Tiller
Michael Tiller

Reputation: 9421

There are two different potential "partial derivatives" you might want. One is the partial derivative with respect to spatial variables (if you are interested in solving PDEs) or you might want the partial derivative of an expression with respect to a simulation variable.

But it doesn't matter, because you cannot express either of these in Modelica.

If your motivation is to solve PDEs, then I'm afraid you will simply have to process the spatial aspects in your models (using some kind of discretization, weak formulation, etc) so that the resulting equations are simple ODEs.

If you want to compute the derivative of expressions with respect to variables other than time, the question would be ... why? I'm hard pressed to think of an application where this is really necessary. But if you can explain your use case, I could comment further on how to handle it.

Upvotes: 2

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