Sean Cohen, North Carolina State University


Efficient Computation of Two-dimensional Plasma Expansion due to Laser Ablation

Abstract: The expansion of plasma resulting from the ablation of a graphite target by a nanosecond laser pulse is effectively modeled by the Navier-Stokes (NS) equations. However, the nature of the initial conditions, in particular the narrow region of extremely high-pressure, high-temperature gas expanding in to a low-pressure, low-temperature atmosphere, presents stability issues to numerical methods. A smoothed approximation of NS is provided by the quasi-gas dynamic (QGD) equations, which have been applied to the computation of laser ablation by Trofimov, et al. This derivation provides a relaxation parameter that is used to manage the computational stability. Finite difference schemes require a large mesh to accurately resolve these solutions. Stability concerns necessitate a time step on the order of the square of the spatial mesh width. The result is a high numerical cost that is prohibitive to computing multi-dimensional problems. In this paper, we apply a high-resolution finite-volume method coupled with an efficient ODE solver to the problem. The finite volume method used is the central-upwind scheme developed by Kurganov et al. Besides more accurate resolution and cost efficiency, the method implemented here allows for more realistic initial conditions that better represent the atmosphere into which the plasma expands. The cost efficiency has allowed us to compute results for the two-dimensional problem. We will show that the scheme is able to compute solutions using NS to model the one-dimensional expansion. We also provide results showing that the relaxation parameter may be chosen independent of the solution, thus simplifying calculations and providing significant numerical savings, while producing results that match those of the NS simulations.

Advisor: Alina Chertock (North Carolina State University)
Collaborators: V. A. Trofimov and I.A. Shirokov (Moscow State University)