An Implicit Discrete Unified Gas-Kinetic Scheme for Simulations of Steady Flow in All Flow Regimes

TL;DR

This paper introduces an implicit version of the discrete unified gas-kinetic scheme (DUGKS) that significantly accelerates steady flow simulations across all flow regimes by employing an implicit solver with LU-SGS and large CFL numbers.

Contribution

The paper develops an implicit DUGKS (IDUGKS) using LU-SGS for faster steady flow simulations across all regimes, improving efficiency by one or two orders of magnitude.

Findings

IDUGKS achieves faster convergence than explicit DUGKS.

Numerical tests validate accuracy across flow regimes.

Efficiency improved by 10 to 100 times.

Abstract

This paper presents an implicit method for the discrete unified gas-kinetic scheme (DUGKS) to speed up the simulations of the steady flows in all flow regimes. The DUGKS is a multi-scale scheme finite volume method (FVM) for all flow regimes because of its ability in recovering the Navier-Stokes solution in the continuum regime and the free transport mechanism in rarefied flow, which couples particle transport and collision in the flux evaluation at cell interfaces. In this paper the predicted iterations are constructed to update the macroscopic variables and the gas distribution functions in discrete microscopic velocity space. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization is applied to solve the implicit equations. The fast convergence of implicit discrete unified gas-kinetic scheme (IDUGKS) can be achieved through the adoption of a numerical time step with large CFL number. Some numerical test cases, including the Couette flow, the lid-driven cavity flows under different Knudsen number and the hypersonic flow in transition flow regime around a circular cylinder, have been performed to validate this proposed IDUGKS. The computational efficiency of the IDUGKS to simulate the steady flows in all flow regimes can be improved by one or two orders of magnitude in comparison with the explicit DUGKS.