The Material Point Method in CSAFE

by
A.N.M. Imroz Choudhury

Advised by
Martin Berzins

The Material Point Method (MPM) is a meshless particle based method for simulating fluid dynamics, solid mechanics, and associated transport problems. It discretizes a problem domain into computational particles which represent the evolving solution to the problem. The particles carry state quantities (such as mass or temperature) with them as they move, which together describe the full state of the system at each timestep. The system is solved by moving the particles in each timestep according to the underlying equations. Visualization follows simply, by using a sphere to represent each particle, colormapped by one or more of the state variables.

We focus on an MPM code designed to solve the advection-diffusion equation in one dimension. We opt to work with this relatively simple problem in order to investigate potentially peculiar features in the problem domain such as sharp boundary fronts, which can produce nonphysical numerical oscillation in the solution. Also, we are interested in the sensitivity of MPM to changes in the density of particles in the initial discretization, as well as the effect of various numerical integration techniques on the outcome of the solution produced by MPM. Overall, we are working toward a better understanding of MPM and how it can fit into the CSAFE project.