Bernoulli Trial (BT) Collision Operator Scheme Family in the Direct Simulation Monte-Carlo (DSMC): Derivation and Evaluation

Francis Padilla; Ehsan Roohi; Stefan Stefanov

doi:10.2478/cait-2026-0011

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Bernoulli Trial (BT) Collision Operator Scheme Family in the Direct Simulation Monte-Carlo (DSMC): Derivation and Evaluation

Cybernetics and Information Technologies

Volume 26 (2026): Issue 2 (June 2026)

By: Francis Padilla, Ehsan Roohi and Stefan Stefanov

Open Access

|Jun 2026

Abstract

The Direct Simulation Monte-Carlo (DSMC) method is based on splitting the rarefied gas process evolution into two ballistic and collision steps within a time step. The collision step is the more complicated, requiring a rigorous theoretical analysis to discover its relation to the fundamental kinetic equations. In this work, we present a systematic derivation and examination of the Bernoulli‑Trial (BT) family of collision schemes. The master Kac equation describes the binary collision interactions as a stochastic process lying in the background of the DSMC probabilistic rules, and it serves as a starting point for our derivation of the BT family. This study is limited to the analysis of four BT members, including Simplified Bernoulli Trials (SBT), Generalized Bernoulli Trials (GBT), Symmetrized Simplified Bernoulli Trials (SSBT), and Symmetrized Generalized Bernoulli Trials (SGBT). These schemes are implemented in the DSMC code, and a simple relaxation problem is simulated to determine optimal values for the pair‑selection parameter N_sel.

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Articles in this issue

DOI: https://doi.org/10.2478/cait-2026-0011 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702

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Language: English

Page range: 3 - 14

Submitted on: Mar 8, 2026

Accepted on: Apr 20, 2026

Published on: Jun 13, 2026

Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies

In partnership with: Paradigm Publishing Services

Keywords:

Direct Simulation Monte-Carlo,

Collision operators,

Mathematical formulation,

Rarefied gas dynamics,

Kinetic theory of gases,

Relaxation processes,

Numerical methods,

Probability Analysis

Related subjects:

Computer sciences,

Information technology

© 2026 Francis Padilla, Ehsan Roohi, Stefan Stefanov, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2026): Issue 2 (June 2026)