Time-dependent Regularized 13-Moment Equations with Onsager Boundary Conditions in the Linear Regime

TL;DR

This paper develops a new set of time-dependent regularized 13-moment equations with Onsager boundary conditions, ensuring stability and accuracy in modeling linear elastic collision systems, verified through numerical channel flow examples.

Contribution

The paper introduces a novel regularized 13-moment model with Onsager boundary conditions that improves stability and removes boundary layers in linear elastic collision systems.

Findings

Equations exhibit super-Burnett order for small Knudsen numbers.

Symmetric structure of the moment equations.

Numerical validation through 1D channel flow simulations.

Abstract

We develop the time-dependent regularized 13-moment equations for general elastic collision models under the linear regime. Detailed derivation shows the proposed equations have super-Burnett order for small Knudsen numbers, and the moment equations enjoy a symmetric structure. A new modification of Onsager boundary conditions is proposed to ensure stability as well as the removal of undesired boundary layers. Numerical examples of one-dimensional channel flows is conducted to verified our model.