I am trying to work out the correct method for recovering a particle’s movement in a vector field, from using the streamline integration of the vector field.

Let’s say I have a vector velocity field. I generate streamlines from this vector field. What is the correct way to recover the particle’s movements from the streamlines?

I want to simulate something like x(t+1) = x (t)+ v*dt where dt is fixed. so I can trace out the particle’s path at fixed time steps.

The streamline points are not extracted at fixed time intervals. I am not quite certain at what time intervals they are at.

I have the points, the velocity at each point and the integration time.

Should I be using the local velocity at each stream line point and multiplying by the difference in integration time to get the new point?

Or, should I be using the differences in points position and dividing by the integration time differences?

I get different results with either method and it is difficult to tie in new calculated positions with the next streamline point.

Any help in how to do this correctly and what are the definitions of integration time and the units involved?