Verification of particle-in-cell simulations with Monte Carlo collisions

Abstract

Widespread recent interest in techniques for demonstrating that computer simulation programs are correct (‘verification’) has been motivated by evidence that traditional development and testing procedures are disturbingly ineffective. Reproducing an exact solution of the relevant model equations is generally accepted as the strongest available verification procedure, but this technique depends on the availability of suitable exact solutions. In this paper we consider verification of a particle-in-cell simulation with Monte Carlo collisions. We know of no exact solutions that simultaneously exercise all of the functions of this code. However, we show here that there can be found in the literature a number of non-trivial exact solutions, each of which exercises a substantial subset of these functions, and which in combination exercise all of the functions of the code. That the code is able to reproduce these solutions is correctness evidence of a stronger kind than has hitherto been elucidated.