DSMC-SPARTA implementation of majorant collision frequency scheme

The direct simulation Monte Carlo (DSMC) method takes a stochastic approach to solving the Boltzmann equation, and is commonly used to model rarefied gas flows. The simulation domain is split into cells, in which computational representative particles mimic the real flow. Since millions to billions of particles need to be tracked, these models need to be both accurate and computationally efficient. Even with high-fidelity collision models, the overall accuracy of the DSMC outcome strongly depends on its ability to predict the correct number of collision events per simulated time step, i.e. the collision frequency. The two most popular approaches for this purpose are the no-time-counter (NTC) and majorant collision frequency (MCF) schemes. While the NTC scheme is designed to reproduce the average collision time for a sufficiently large sample sizes, the MCF scheme has the advantage of reproducing the exact Poisson distribution of collision time as well as the mean collision time with a reduced sample size. Both schemes have linear complexity of O(N), with N being the number of particles. In this work, we implement the MCF scheme in SPARTA, an open source DSMC solver. A series of numerical tests are performed to illustrate the efficiency and accuracy of both the schemes. Various benchmarks highlighting unsteady, compression, and expansion problems are studied.