Simplification of the unified gas kinetic scheme

Abstract

The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.

Entropy Conditions Involved in the Nonlinear Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows

“…Good agreement between the NCCM and the NSF Tw=290 K. The Knudsen number is defined as the ratio of mean free path to the length of cavity side wall, 1 and the mean free path of gas is evaluated for a hard sphere model. Similar to the previous work [29] …”

“…The heat fluxes around the solid surface are given in Figure 6. Good agreement of the results of the NCCM and the DSMC and UGKS (Unified gas-kinetic scheme) methods [29] was observed. These two cases are of a high Kn number and in the region of far-equilibrium states.…”

“…The contours of Ma number, density, and heat flux are shown in Figure 5; typical T w =290 K. The Knudsen number is defined as the ratio of mean free path to the length of cavity side wall, 1 and the mean free path of gas is evaluated for a hard sphere model. Similar to the previous work [29], the wall 2 velocity is for cases at Kn=0.671 and 6.712. The solutions are compared with the DSMC ones.…”

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

“…Subsequent study [16] addressed the status of the used quantum optical master equation and found similar effects using just a Pauli rate equation, describing the working principle of Scully's model by a purely classical stochastic process (master equation where the coherences decouple from populations was derived after performing a polaron transformation). Recently, another study appeared treating a further refined model numerically, considering also non-Markovian effects due to the coupling of the system to a highly correlated environment [17]. Still, the exact mechanism of the effect remains somewhat unclear which makes it difficult to predict if it will be relevant in other setups and what the essential ingredients of such setups might be.…”

Progress of discrete unified gas-kinetic scheme for multiscale flows

“…We now make an analysis of the difference between the reconstructed time-averaged interface distribution functions in the UGKS and DUGKS. Specifically, if physical quantities are assumed to be linearly distributed around the cell, we can obtain the structure off x jk , ξ in UGKS based on the results in [70] as follows,…”