Collision Computation Of Moving Bodies

In this paper, an explicit mathematical representation of n-dimensional bodies moving in translation along general trajectories is derived. This representation is used to find out if two moving bodies are going to collide. An optimization problem is developed for finding the time and location of collision. We consider the special cases of linear and piecewise linear trajectories. The collision in this case can be obtained by solving a linear program or a sequence of linear programs, respectively. The problem of finding the collision time and location of several moving bodies is cast as an integer programming problem. A comprehensive simulation study shows that this approach requires much lesser computation time when compared with the current approach of finding the collision between all pairs of bodies

Numerical simulation of moving rigid body in rarefied gases

In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton-Euler equations, where the force and the torque on the rigid body is computed from the momentum transfer of the gas molecules colliding with the body. On the other hand, the motion of the rigid body influences the gas flow in its surroundings. We validate the numerical results by testing the Einstein relation for Brownian motion of the suspended particle. The translational as well as the rotational degrees of freedom are taken into account. It is shown that the numerically computed translational and rotational diffusion coefficients converge to the theoretical values.Comment: 16 pages, 8 figure