Spatio-temporal error coupling and competition in meso-flux construction of discrete unified gas-kinetic scheme

Abstract

This research systemically studies the numerical characteristics of the discrete unified gas-kinetic scheme (DUGKS) in terms of tracking interface motions driven by prespecified velocity fields. Multiple reconstruction methods have been utilized for the meso-flux construction of DUGKS and the performance of each method is evaluated accordingly. The spatio-temporal error coupling mechanism exhibited in the meso-flux evaluation is identified and analyzed theoretically for the first time. The spatio-temporal error competition mechanism (STECM) appeared during the construction of upwind meso-flux is specifically illustrated and discussed. On the basis of the newly discovered mechanism, we propose a high-resolution DUGKS by employing the fourth-order reconstruction scheme and the one-stage marching technique. Four benchmark tests have been conducted and numerical results have demonstrated the superiority of this high-resolution DUGKS over the lattice Boltzmann method (LBM) in capturing dynamic interfaces. Comparative results have also revealed that the STECM profoundly impacts the overall resolution of DUGKS implemented with different cell-based reconstruction methods. The STECM provides a theoretical understanding of the spatio-temporal characteristics of numerical errors of DUGKS and could serve as helpful guidance for the design of high-resolution DUGKS in future research.