# What is Direct Simulation Monte Carlo and why is it a good method for simulating spacecraft drag in VLEO?

Reducing spacecraft drag in Very Low Earth Orbit through shape optimisation J. A. Walsh and L. Berthoud (2017) show simulations calculating drag coefficients for different "nose cone" shapes of spacecraft in Very Low Earth Orbit or VLEO. It says:

In order to answer this question, it is necessary to perform aerodynamic simulations on the satellite body. The atmospheric density in VLEO is so low that the medium is no longer continuous, but can rather be described as a molecular flow (Knudsen Number>1),8 for which there are a number of simulation methods available. These include analytical methods such as those presented by Sentman8 Analytical methods can provide fast estimates of the aerodynamic forces a body might experience but are less useful with more complex shapes, especially where secondary particle-surface interactions occur9. Alternatively, particle simulators such as the Direct Simulation Monte Carlo (DSMC) methods pioneered by Bird10 can provide a more accurate assessment of the aerodynamic forces as they endeavour to replicate the physics behind molecular flow. However, this comes at the cost of longer simulation time. For the work being performed here, the ability to capture the non-linear aspects of the flow around complex bodies is desirable. For this reason the DSMC code ’SPARTA’ (which stands for Stochastic PArallel Rarefied-gas Time-accurate Analyzer)11,12 was used.

Question: What is Direct Simulation Monte Carlo and why are "particle simulators" like this a good method for simulating spacecraft drag in VLEO?

Table 1: Atmospheric Properties in VLEO

Minimum      Maximum      Simulation
Density [kg/m3 ]   7.28×10E−12   2.49×10E−09   1.05×10E−10
Temperature [°K]       447          1438           990
Velocity [km/s]       7.70          7.85          7.77


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## 1 Answer

My understanding is that the "Direct Simulation" part refers to the fact that rather than solving equations governing the flow (as in Computational Fluid Dynamics) it directly simulates the particles interacting with the surfaces. Rather than modelling each atom, they are grouped into "molecules" representing a large number of atoms, and the result of each interaction is calculated based on probabilistic models. Information on the SPARTA tool can be found here.

This approach is used in VLEO analysis because the very low density (and high temperature) means that the mean-free-path of the atmospheric particles is much much larger than the dimensions of satellite. This means that there is almost no interaction between the particles themselves, so the concepts of "flow" and fluid dynamics don't really apply.

• Thank you for your informative and sourced answer, and Welcome to Space! It sounds like a straight forward Monte Carlo simulation but with some tricks to speed it up over a zillion independent atoms. – uhoh Feb 10 at 10:54
• This is a nice answer: You might want to add a reference to the Wikipiedia entry for DSMC and also Knudsen number (which I only just discovered). – tfb Feb 10 at 15:33