NRxx Simulation of Microflows with Shakhov Model

TL;DR

This paper introduces a simulation approach for microflows using the NRxx method combined with the Shakhov model, addressing boundary conditions and demonstrating convergence through numerical examples.

Contribution

It develops a uniform framework for different order moment systems with wall boundary conditions in microflow simulations.

Findings

Demonstrates convergence with increasing moments

Validates the method with steady and unsteady problems

Addresses boundary condition challenges in moment methods

Abstract

In this paper, we propose a method to simulate the microflows with Shakhov model using the NRxx method developed in [4, 5, 6]. The equation under consideration is the Boltzmann equation with force terms and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.