A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Johannes Krotz, Cory D. Hauck, Ryan G. McClarren

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. From a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

Original languageEnglish
Article number113253
JournalJournal of Computational Physics
Volume514
DOIs
StatePublished - Oct 1 2024

Keywords

  • Hybrid stochastic-deterministic method
  • Kinetic equations
  • Monte Carlo
  • Particle transport

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