In the last decade a significant advance has been made in understanding the behaviour of small heavy particles advected by turbulent flows. There are two principal motivations to study such problem. One is to understand rain formation and the second is to understand the formation of planets in a circumstellar disk. In both of these cases the crucial question is whether small objects can collide (frequently enough, in the right range of relative speeds) to eventually merge and form bigger objects -- raindrop in one case and planetesimals in the other.
Most of the work has concentrated on study of small spherical objects. The behaviour of non-spherical but still small heavy objects can potentialy be quite different from spherical ones. Note further that although raindrops are to a good approximation spherical, the astrophysical dust is not. Our aim in this project is to study clustering and possible collisions between non-spherical objects.
The simplest model of a non-spherical object would be an ellipsoid. Let us start by considering an ellipsoid with three principal axis. In what follows, we shall call an ellipsoid "a grain". We shall start by making the following approximations:
We would then have to solve the following numerical problem. The instantaneous velocity and angular velocity of a grain and the local velocity and its gradients (strain and vorticity) sets the drag for and drag torque. These are given the by the Jeffery's equation. With the force and torque thus determined, we need to solve the equation of motion of a rigid body. This last step is best done by using the quaternions to describe the rigid body rotations.
The aim of the project is to calculate the following quantities:
We have a code that solves this problem. The time-stepping is done by a Runge-Kutta fourth order method. The code is written in C++ . As each grain is independent of every other grain this problem is ripe for extreeme parallelisation. We have now written a CUDA code to solve the problem in GPU. We have already tested the code in GPU machines. We expect that the problem would require averaging over very large number of snapshots. We also need to scan a large range of parameters in terms of (a) the shape of the grains (b) their stokes number which is a ratio of the stopping time of a grain to characteristic time scale of flow.
This work is a collaboration between myself, Akshay Bhatnagar and Dario Vincenzi.