Optimizing Sparse Representations of Kinetic Distributions via Information Theory
Technical Report,09 Jun 2017,31 Jul 2017
Air Force Research Laboratory (AFMC) AFRL/RQRS Edwards AFB United States
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This project is on the use of ideas from information theory in the kinetic simulation of a gas or plasma. A kinetic simulation describes the interactions i.e., collisions and convection of particles that constitute a gas or plasma. Since the number of physical particles is often much too large e.g., 1020 for direct molecular dynamics computations, kinetic simulation often uses a moderate number, N e.g.,105-107, representative computational macro-particles which act as surrogates for the particle interactions. The particle positions, xn, and velocities, vn, for n ranging from 1 to N, are a representative sample of a probability distribution function fx v. Traditionally, these macro-particles have all represented a constant number of real particles with a particle shape which is a single Dirac-delta function velocity and either delta functions in space or low order splines dependent on the spatial resolution sought as described in more detail in Bridsalls classic reference 1. This sparse sampling of f results in a direct trade-off between spatial accuracy and statistical noise for key flow-field parameters such as mass, momentum, energy, and physical entropy.
- Numerical Mathematics