High order discrete unified gas kinetic scheme with multi-moment constrained conservative semi-Lagrangian reconstruction

Abstract

In this work, a high-order discrete unified gas kinetic (HDUGKS) scheme for multiscale gas flows was presented. The proposed scheme is a high-order finite volume method, which holds good conservation property of the scheme. Moreover, in the proposed scheme, the high-order accuracy was achieved by a constrained interpolation profile conservative semi-Lagrangian (CIP-CSL) reconstruction, where both point values (PVs) and volume-integrated averages (VIAs) are defined and used to fulfill a compact reconstruction of high order polynomials in a local finite volume cell. The PVs are updated using semi-Lagrangian scheme along the characteristics of the kinetic model equations to maintain high efficiency and low numerical dissipation, but the VIAs are evolved under the discrete unified gas kinetic scheme (DUGKS) framework to preserve the conservation. To demonstrate the idea of the HDUGKS, a cubic polynomial reconstruction based one-dimensional HDUGKS was presented. Furthermore, the high order accuracy property of the proposed scheme was evaluated by five one-dimensional numerical benchmarks including: (a) 1-D sine wave, (b) shock structure, (c) Sod’s shock tube problem, (d) Lax shock tube problem, (e) Shu-Osher problem, and the numerical results show that, while there is one order of accuracy reduction in the proposed scheme due to the low order semi-Lagrangian updating of the PVs, the proposed scheme can almost achieve third order accuracy and obtain more accurate results with fewer meshes than the DUGKS. Additionally, the numerical results indicate that the present method maintains the multiscale properties of the original DUGKS and serve as an efficient numerical method for flow simulations in all Knudsen number flow regime as well.