A third-order discrete unified gas kinetic scheme for continuum and rarefied flows: low-speed isothermal case

TL;DR

This paper introduces a third-order discrete unified gas kinetic scheme (DUGKS) that achieves high accuracy and efficiency in simulating both continuum and rarefied flows, overcoming limitations of previous second-order methods.

Contribution

The paper presents a novel third-order DUGKS with two-stage time-stepping and high-order flux reconstruction, capable of handling rarefied flows and surpassing existing methods in accuracy and efficiency.

Findings

Third-order accuracy in time and space achieved.

Outperforms second-order DUGKS in accuracy and flow detail capture.

Efficiently simulates rarefied flows with improved results.

Abstract

An efficient third-order discrete unified gas kinetic scheme (DUGKS) with efficiency is presented in this work for simulating continuum and rarefied flows. By employing two-stage time-stepping scheme and the high-order DUGKS flux reconstruction strategy, third-order of accuracy in both time and space can be achieved in the present method. It is also analytically proven that the second-order DUGKS is a special case of the present method. Compared with the high-order lattice Boltzmann equation {LBE} based methods, the present method is capable to deal with the rarefied flows by adopting the Newton-Cotes quadrature to approximate the integrals of moments. Instead of being constrained by the second-order (or lower-order) of accuracy in time splitting scheme as in the conventional high-order Runge-Kutta (RK) based kinetic methods, the present method solves the original BE, which overcomes the limitation in time accuracy. Typical benchmark tests are carried out for comprehensive evaluation of the present method. It is observed in the tests that the present method is advantageous over the original DUGKS in accuracy and capturing delicate flow structures. Moreover, the efficiency of the present third-order method is also shown in simulating rarefied flows.