Models of Thermal Relaxation Mechanics for Particle Simulation Methods

Abstract

An improved phenomenological microscopic model is introduced in the present study and compared to existing models for simulating molecular vibrational relaxation in rarefied flows. These models are employed in statistical particle simulation methods such as the direct simulation Monte Carlo (DSMC) technique. In the traditional Borgnakke-Larsen model, collision energies are partitioned among contributing energy modes as dictated by fractions sampled from equilibrium distributions. Application of this method to fully excited continuous energy modes alone, such as in translation-rotation (T-R) exchange, promotes the equilibrium state. However, application to translation-vibration (T-V) exchange is afforded by unrealistically approximating the quantized distribution as continuous and partially excited, and employing individual collision "temperatures" in an attempt to capture the temperature-dependence of the necessary distributions. As proven in theoretical and numerical analyses, such an implementation of the Borgnakke-Larsen method may fail to promote the equilibrium relaxed state exactly and poses computational difficulties. The improved technique of the present work iterates between translation-rotation and rotation-vibration exchanges which does promote equilibrium exactly if the model for the latter process is compatible with quantized oscillators. This may be achieved by quantizing the total internal energy of a molecule and dividing the quanta randomly among the rotational and vibrational energy modes. This iteration-equipartition model retains computational simplicity and promotes thermal equilibrium even when applied to multi-species gas mixtures of non-degenerate anharmonic quantized oscillators.