Gaussian Mixture Model Solvers for the Boltzmann Equation
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.
- Research Organization:
- Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
- DOE Contract Number:
- NA0003525
- OSTI ID:
- 2402991
- Report Number(s):
- SAND--2022-13436
- Country of Publication:
- United States
- Language:
- English
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