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Residence time in the particle tracing module

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I ran a simulation of a polymeric solution inside an extrusion die by using laminar flow and carreau model. Afterwards, I implemented the particle tracing module, beacuse I am interested in the residence time which is the time a particle takes to exit the die.

Does anybody know how to add the auxiliary dependent variable: d(rp)/dt = 1 in the particle tracing module?

Somebody told me that this will solve the additional ODE per particle, and rp is the residence time.

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