离散时空直接建模思想及其在模拟多尺度输运中的应用

刘畅; 徐昆

doi:10.7638/kqdlxxb-2020.0018

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离散时空直接建模思想及其在模拟多尺度输运中的应用

综述 | 更新时间：2026-05-28

- 离散时空直接建模思想及其在模拟多尺度输运中的应用
- Direct modeling methodology and its applications in multiscale transport process
- 空气动力学学报 2020年38卷第2期页码：197-216
- 作者机构：
  
  1. 香港科技大学数学系,香港
  2. 香港科技大学深圳研究院,深圳,518057
- 作者简介：
  
  刘畅(1990-), 男, 河南濮阳人, 博士, 主要研究方向:稀薄气体动理学, 气体动力学, 等离子体输运、光子输运等的多尺度输运过程.E-mail:cliuaa@connect.ust.hk
  徐昆*(1966-), 男, 博士, 讲座教授, 主要研究方向:计算流体力学高精度格式, 稀薄气体动理学, 输运问题的多尺度建模等.E-mail:makxu@ust.hk
- 基金信息：
- DOI：10.7638/kqdlxxb-2020.0018
  中图分类号： V211.3
- 纸质出版：2020
- 稿件说明：
移动端阅览
刘畅, 徐昆. 离散时空直接建模思想及其在模拟多尺度输运中的应用[J]. 空气动力学学报, 2020, 38(2): 197-216.

LIU Chang, XU Kun. Direct modeling methodology and its applications in multiscale transport process[J]. 2020, 38(2): 197-216.
刘畅, 徐昆. 离散时空直接建模思想及其在模拟多尺度输运中的应用[J]. 空气动力学学报, 2020, 38(2): 197-216. DOI： 10.7638/kqdlxxb-2020.0018.

LIU Chang, XU Kun. Direct modeling methodology and its applications in multiscale transport process[J]. 2020, 38(2): 197-216. DOI： 10.7638/kqdlxxb-2020.0018.

摘要

统一气体动理学格式是基于离散空间直接建模的思想构建的多尺度数值格式。本文对统一气体动理学格式近十年的发展进行总结，并对未来的发展方向进行展望。统一气体动理学格式的建模思路突破了传统偏微分方程数值离散求解的制约，回归物理建模的出发点，基于守恒定律在离散时空有限尺度的控制体上进行建模，利用网格界面处的动理学方程时间演化解构建数值通量，从而构造出有限控制体上取决于网格尺度和时间步长的气体动力学控制方程。统一气体动理学格式建模有两个关键点：一是宏观守恒量与微观分布函数耦合演化，二是通过界面处的多尺度时间演化解构建数值通量。统一气体动理学格式是一种多尺度数值格式，根据网格努森数能够准确捕捉从稀薄到连续不同流域的流体物理。从某种意义上说气体动理学格式提供了有效的随不同网格努森数变化的连续性方程，即连续流的纳维-斯托克斯（N-S）方程和稀薄流的波尔兹曼（Boltzmann）是统一气体动理学格式在网格努森数很小和很大情况小逼近的两个极限方程。对于连续流的黏性边界层问题的捕捉，统一动理学格式不要求网格尺度小于粒子平均自由程。统一气体动理学格式成功应用于多尺度气体输运，等离子体输运，中子、光子输运，以及气固离散两相流等领域的数值模拟，在计算精度和计算效率上都体现出明显优势。尤其对于等离子体的输运计算，统一气体动理学格式提供了一个在连续变化尺度上的模拟方法，包括从求解电子、离子的自由输运的Vlasov动理学方程到连续流域内的双流体方程以及磁流体方程。本文总结了统一气体动理学格式的建模思想，数值性质，以及格式在不同领域的应用。

Abstract

The direct modeling methodology provides a framework for multiscale modeling of transport processes

based on which the unified gas kinetic scheme (UGKS)

the discrete unified kinetic scheme (DUGKS)

and unified gas kinetic wave-particle (UGKWP) method have been developed over the last decade. The methodology of direct modeling is to construct the numerical governing equations on a discrete control volume by taking into account the contribution of both particle transport and collision process. The two important ingredients of the direct modeling methodology are the coupling evolution of the macroscopic quantities and microscopic distribution function

and the utilization of the local evolution solution in the construction of numerical flux. Based on the direct modeling methodology

we construct a continuous spectrum of governing equations in the whole flow regimes

which automatically recovers the collision-less Boltzmann and Navier-Stokes equations in their corresponding limiting regimes. In this paper

we are going to review the direct modeling methodology

the construction of schemes

and the multiscale and unified preserving properties. We will also review the applications of the schemes in the transport process of gas

plasma

photon

and disperse multiphase flow

and give an outlook of the future developments.

关键词

Keywords

references

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