HOMEWORK: 21 February. Write a 2D molecular dynamics routine, in a shear cell (so periodic on the sides, shearing top and bottom). Use either a "soft particle" or truncated LJ potential, with an average density of about 0.5. Parallelize over cells (if using bins), or over particles (if using neighbor lists). How many particles are needed to get a reasonable velocity profile? In molecular dynamics, we abandon the continuum framework. Instead, we model the motion of particles, or maybe pseudo-particles, as they interact. One can think of long-range forces, or short-range forces. For now, lets consider only short-range forces.

MD comes in two basic flavors

1. Event Driven MD. For relatively low density flows, it makes sense to proceed from collision time to collision time, if one assumed the only collisions were two particle collisions. If one knew the location and velocities of all particles, and if one assumes particles free-stream between collisions, then one could solve for the next time any pair of particles will collide. Advance to that time. Assume the particles as rigid, so the collision is instanteneous. At the time of collision, knowing the incoming momentum and energy of the colliding pair, one can solve for the outgoing momentum and energy - and thus for the velocities.
2. Soft Particle MD. Newton's laws tell us f=ma. So, viewing this as a 2nd-order ODE for each particle, lets integrate the equations numerically. The forces are comprised of all pairwise interactions. So compute the forces, given current configuration, and use a decent (i.e., at least 2nd-order accurate) numerical method to update the positions and velocities.

For our purposes now, lets limit discussion to soft particle methods.

• Classic MD
  • Interaction Arrays
  • Long Range Forces
• Monte Carlo Methods
• About this document ...