Finding the Force -- Consistent Particle Seeding for Satellite Aerodynamics

Abstract

When calculating satellite trajectories in low-earth orbit, engineers need to adequately estimate aerodynamic forces. But to this day, obtaining the drag acting on the complicated shapes of modern spacecraft suffers from many sources of error. While part of the problem is the uncertain density in the upper atmosphere, this works focuses on improving the modeling of interacting rarified gases and satellite surfaces. The only numerical approach that currently captures effects in this flow regime---like self-shadowing and multiple molecular reflections---is known as test-particle Monte Carlo. This method executes a ray-tracing algorithm to follow particles that pass through a control volume containing the spacecraft and accumulates the momentum transfer to the body surfaces. Statistical fluctuations inherent in the approach demand particle numbers in the order of millions, often making this scheme too costly to be practical. This work presents a parallel test-particle Monte Carlo method that takes advantage of both GPUs and multi-core CPUs. The speed at which this model can run with millions of particles allowed exploring a regime where a flaw in the model's initial particle seeding was revealed. Our new model introduces an analytical fix based on seeding the calculation with an initial distribution of particles at the boundary of a spherical control volume and computing the integral for the correct number flux. This work includes verification of the proposed model using analytical solutions for several simple geometries and demonstrates uses for studying aero-stabilization of the Phobos-Grunt Martian probe and pose-estimation for the ICESat mission.