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Kinetic solvers with adaptive mesh in phase space.

Robert R Arslanbekov1, Vladimir I Kolobov1, Anna A Frolova2

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An adaptive mesh in phase space (AMPS) methodology efficiently solves kinetic equations using a novel tree data structure. This approach reduces computational cost and memory usage for complex simulations.

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Area of Science:

  • Computational Physics
  • Kinetic Theory
  • Numerical Methods

Background:

  • Solving multidimensional kinetic equations is computationally intensive.
  • Existing methods often require significant memory and processing power.
  • Adaptive mesh techniques can potentially optimize resource allocation.

Purpose of the Study:

  • To introduce and validate the adaptive mesh in phase space (AMPS) methodology.
  • To demonstrate AMPS's efficiency in solving kinetic equations.
  • To showcase AMPS's applicability across various physical systems.

Main Methods:

  • Developed a "tree of trees" (ToT) data structure for Cartesian meshes in configuration (r) and velocity (v) spaces.
  • Implemented dynamic adaptation of the r mesh around embedded boundaries and on-the-fly v mesh generation.
  • Utilized importance sampling, multipoint projection, and variance reduction for collision integrals.

Main Results:

  • Successfully solved full and linear Boltzmann equations using AMPS.
  • Developed efficient algorithms for discrete Boltzmann collision integrals.
  • Demonstrated AMPS in simulations of rarefied gas flows, plasma kinetics, radiation transport, and semiconductor electron streaming.

Conclusions:

  • AMPS offers a computationally efficient solution for multidimensional kinetic equations.
  • The methodology significantly reduces computational cost and memory requirements.
  • AMPS is a versatile technique applicable to diverse scientific and engineering problems.