Dear Friends,

When we are using finite difference method we get the numerical values of the basic fluid parameters like temperature, velocity, density on the grid points.

But is there any way to follow a particluar fulid-element so that we know that this particular element was at position (x1,y1,z1) at time t1, its has moved to point (x2,y2,z2) at time t2 and so on?

For example, for a flow past cylinder, suppose i want to know that if partcular element is at a particular position when it is quite far away from the cylinder and then i want to know where it will be after passing the cylinder. What is the method to find this?

Thankx Yogesh

If you have the velocity field (on the Eulerian grids) for _every_ timestep, then it is a simple matter to "inject" fluid particles at any position and watch their Lagrangian evolution in time. If you don't have data for every timestep, you can still visualize particle trajectories, but quite inaccurately.

Basically, you'd apply: dx/dt = u

So if you have the local velocity u and the position x of the particle at time t, you can integrate the above equation to find the new position at the new time t+dt.

Most/all visualization packages already have this capability in the code. You would just have to click at a position to start the "particle injection" and watch its evolution.

One warning to you though. For this "post-processed" visualization process to be half-way decent you need high grid density, and higher order time integration.

Check the JCP paper by Robert Haimes (post 1990) which discusses accuracy issues in time integration for visualization, etc. Very good paper.

Adrin Gharakhani