A simplified unified wave-particle method for diatomic gases with rotational and vibrational non-equilibrium

TL;DR

This paper introduces a simplified unified wave-particle (SUWP) method for simulating diatomic gases with rotational and vibrational non-equilibrium in hypersonic flows, combining kinetic and macroscopic models for improved efficiency.

Contribution

The paper develops a novel SUWP method based on a QMC mechanism, integrating a three-temperature model and collisionless DSMC to efficiently simulate non-equilibrium diatomic gas flows.

Findings

The SUWP method accurately predicts shock structures and flow fields.

It demonstrates computational efficiency comparable to DSMC.

Validation against benchmark cases confirms its effectiveness.

Abstract

The hypersonic flow around near-space vehicles constitutes a multi-scale flow problem. Due to insufficient molecular collisions to achieve equilibrium, rarefied gas effects are present in the flow field. Thus, numerical methods capable of accurately resolving multi-scale flows are required. Furthermore, high-temperature gas effects in hypersonic flows mean vibrational excitation of polyatomic molecules. Consequently, numerical methods accounting for non-equilibrium in rotational and vibrational internal energy modes are required. This study derives a quantified model-competition (QMC) mechanism for diatomic gases with rotational and vibrational non-equilibrium, starting from integral solutions of kinetic model equations with rotational and vibrational energy. The QMC mechanism categorize collisional and free-transport particles in cell, applying computational weighting based on their local scale regimes. We developed a simplified unified wave-particle (SUWP) method for diatomic gases based on QMC mechanism. For the macroscopic of the method, a three-temperature model accounting for rotational and vibrational energy is incorporated into both the kinetic inviscid flux scheme and {Navier-Stokes} solvers. For the microscopic of the method, a collisionless DSMC solver is employed to resolve non-equilibrium flow physics. This work validates the proposed SUWP method with rotational and vibrational non-equilibrium through benchmark cases, including shock tube, shock structures, flow past a cylinder, Apollo 6 command module and space station Mir. Compared to the DSMC and deterministic methods, the SUWP method exhibits favorable computational efficiency while maintaining accuracy.