Performance evaluation of high-order reconstruction for discrete unified gas-kinetics scheme in tracking fluid interfaces

TL;DR

This paper evaluates high-order reconstruction methods within the discrete unified gas-kinetics scheme (DUGKS) for tracking complex fluid interfaces, revealing their impact on accuracy and efficiency in microfluidic modeling.

Contribution

It introduces high-order isotropic finite-difference schemes into DUGKS and assesses the performance of third-stage third-order DUGKS with source terms, providing insights into their advantages and limitations.

Findings

High-order schemes reduce numerical dissipation in DUGKS.

The overall accuracy is limited by source term prediction precision.

Third-stage third-order DUGKS is constrained by the ratio of time step to collision time.

Abstract

With a noticeable increase in research centered on modeling micro fluid interfaces in the framework of mesoscopic methods, we conduct an exhaustive study of discrete unified gas-kinetics scheme (DUGKS) in handling complicated interface deformations. High-order isotropic finite-difference schemes are first utilized in DUGKS to improve its capability in tracking interfaces. The performance of third-stage third-order DUGKS where source term is incorporated has also been assessed for the first time and a series of numerical tests have been conducted to investigate their capability. The comparative analysis have revealed the reason why the performance of lattice Boltzmann method is superior to that of discrete velocity method and DUGKS in general condition from an informed perspective. The mechanism behind the performance distinction between the central scheme and upwind scheme utilized in meso-flux construction in DUGKS have also been clarified. Numerical results have shown that the employment of high-order schemes in DUGKS does have an effect on the reduction of numerical dissipation, but the overall accuracy of this method is limited by the precision of prediction of source terms on mesh interface. The capability of third-stage third-order DUGKS is severely inhibited by its intrinsic limitation of the ratio of time step to particle collision time. Among the various kinds of DUGKS employed with different reconstruction methods, the most promising scheme is the one with third-order isotropic reconstruction and upwind-based meso-flux evaluation, which is able to ensure an unique balance between efficiency and accuracy.