Progress of discrete unified gas-kinetic scheme for multiscale flows

AbstractMultiscale gas flows appear in many fields and have received particular attention in recent years. It is challenging to model and simulate such processes due to the large span of temporal and spatial scales. The discrete unified gas kinetic scheme (DUGKS) is a recently developed numerical approach for simulating multiscale flows based on kinetic models. The finite-volume DUGKS differs from the classical kinetic methods in the modeling of gas evolution and the reconstruction of interface flux. Particularly, the distribution function at a cell interface is reconstructed from the characteristic solution of the kinetic equation in space and time, such that the particle transport and collision effects are coupled, accumulated, and evaluated in a numerical time step scale. Consequently, the cell size and time step of DUGKS are not passively limited by the particle mean-free-path and relaxation time. As a result, the DUGKS can capture the flow behaviors in all regimes without resolving the kinetic scale. Particularly, with the variation of the ratio between numerical mesh size scale and kinetic mean free path scale, the DUGKS can serve as a self-adaptive multiscale method. The DUGKS has been successfully applied to a number of flow problems with multiple flow regimes. This paper presents a brief review of the progress of this method.

Download Full-text

An Implicit Unified Gas Kinetic Scheme for Radiative Transfer with Equilibrium and Non-Equilibrium Diffusive Limits

Communications in Computational Physics ◽

10.4208/cicp.oa-2016-0261 ◽

2017 ◽

Vol 22 (4) ◽

pp. 889-912 ◽

Cited By ~ 12

Author(s):

Wenjun Sun ◽

Song Jiang ◽

Kun Xu

Keyword(s):

Radiative Transfer ◽

Nonlinear Diffusion ◽

Kinetic Scheme ◽

Diffusion Limit ◽

Radiative Transport ◽

Time Step ◽

Equilibrium Limit ◽

Unified Gas Kinetic Scheme ◽

Material Temperature ◽

Non Equilibrium

AbstractThis paper is about the construction of a unified gas-kinetic scheme (UGKS) for a coupled system of radiative transport and material heat conduction with different diffusive limits. Different from the previous approach, instead of including absorption/emission only, the current method takes both scattering and absorption/emission mechanism into account in the radiative transport process. As a result, two asymptotic limiting solutions will appear in the diffusive regime. In the strong absorption/emission case, an equilibrium diffusion limit is obtained, where the system is mainly driven by a nonlinear diffusion equation for the equilibrium radiation and material temperature. However, in the strong scattering case, a non-equilibrium limit can be obtained, where coupled nonlinear diffusion system with different radiation and material temperature is obtained. In addition to including the scattering term in the transport equation, an implicit UGKS (IUGKS) will be developed in this paper as well. In the IUGKS, the numerical flux for the radiation intensity is constructed implicitly. Therefore, the conventional CFL constraint for the time step is released. With the use of a large time step for the radiative transport, it becomes possible to couple the IUGKS with the gas dynamic equations to develop an efficient numerical method for radiative hydrodynamics. The IUGKS is a valid method for all radiative transfer regimes. A few numerical examples will be presented to validate the current implicit method for both optical thin to optical thick cases.

Download Full-text

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

Advances in Aerodynamics ◽

10.1186/s42774-019-0026-3 ◽

2020 ◽

Vol 2 (1) ◽

Cited By ~ 3

Author(s):

Xinliang Song ◽

Chuang Zhang ◽

Xiafeng Zhou ◽

Zhaoli Guo

Keyword(s):

Heat Transfer ◽

Radiative Heat Transfer ◽

Radiative Heat ◽

Kinetic Scheme ◽

Mean Free Path ◽

Anisotropic Scattering ◽

Scattering Media ◽

Unified Gas Kinetic Scheme ◽

Free Transport ◽

Scattering Phase Function

AbstractIn this work, a discrete unified gas kinetic scheme (DUGKS) is developed for radiative transfer in anisotropic scattering media. The method is an extension of a previous one for isotropic radiation problems [1]. The present scheme is a finite-volume discretization of the anisotropic gray radiation equation, where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion. With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces, the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime. Several one- and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS, and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.

Download Full-text

Micro- and Nanoscale Conductive Tree-Structures for Cooling a Disk-Shaped Electronic Piece

Journal of Heat Transfer ◽

10.1115/1.4007903 ◽

2013 ◽

Vol 135 (3) ◽

Cited By ~ 27

Author(s):

Masoud Daneshi ◽

Marjan Zare ◽

Mohammad Reza Salimpour

Keyword(s):

Free Path ◽

Heat Conductivity ◽

Analytical Method ◽

Electronic Devices ◽

Mean Free Path ◽

Numerical Approach ◽

Small Scale ◽

Conductive Heat ◽

Tree Structures ◽

Conductive Material

In this research, we consider the generation of conductive heat trees at microscales and nanoscales for cooling electronics which are considered as heat-generating disk-shaped solids. With the advent of nanotechnology and the production of electronics in micro- and nanoscales in recent years, designing workable systems for cooling them is considered widely. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loops are generated for cooling such electronic devices. Furthermore, constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. Since there are some constructal tree architectures which are not possible to be generated analytically, numerical approach is used for optimization. When the smallest features of the internal structure are smaller than mean free path of the energy carriers, heat conductivity is no longer a constant and becomes a function of the smallest dimension of the structure. Therefore, we consider models which were proposed for estimating conductivity of small scale bodies.

Download Full-text

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations

Communications in Computational Physics ◽

10.4208/cicp.190912.080213a ◽

2013 ◽

Vol 14 (5) ◽

pp. 1147-1173 ◽

Cited By ~ 55

Author(s):

Juan-Chen Huang ◽

Kun Xu ◽

Pubing Yu

Keyword(s):

Distribution Function ◽

Kinetic Scheme ◽

Particle Collision ◽

Gas Distribution ◽

Time Step ◽

Rarefied Flow ◽

Low Speed ◽

Flow Computation ◽

Unified Gas Kinetic Scheme ◽

Non Equilibrium

AbstractDue to the rapid advances in micro-electro-mechanical systems (MEMS), the study of microflows becomes increasingly important. Currently, the molecular-based simulation techniques are the most reliable methods for rarefied flow computation, even though these methods face statistical scattering problem in the low speed limit. With discretized particle velocity space, a unified gas-kinetic scheme (UGKS) for entire Knudsen number flow has been constructed recently for flow computation. Contrary to the particle-based direct simulation Monte Carlo (DSMC) method, the unified scheme is a partial differential equation-based modeling method, where the statistical noise is totally removed. But, the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space. Due to the multiscale modeling in the unified method, i.e., the update of both macroscopic flow variables and microscopic gas distribution function, the conventional constraint of time step being less than the particle collision time in many direct Boltzmann solvers is released here. The numerical tests show that the unified scheme is more efficient than the particle-based methods in the low speed rarefied flow computation. The main purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena. In the continuum and free molecular limits, the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions. In the transition regime, the DSMC solution will be used for the validation of UGKS results. This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows. It not only recovers the DSMC results whenever available, but also provides high resolution results in cases where the DSMC can hardly afford the computational cost. In thermal creep flow simulation, surprising solution, such as the gas flowing from hot to cold regions along the wall surface, is observed for the first time by the unified scheme, which is confirmed later through intensive DSMC computation.

Download Full-text

Unified gas-kinetic wave-particle methods IV: multi-species gas mixture and plasma transport

Advances in Aerodynamics ◽

10.1186/s42774-021-00062-1 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Chang Liu ◽

Kun Xu

Keyword(s):

Free Path ◽

Cell Size ◽

Knudsen Number ◽

Mean Free Path ◽

Plasma Transport ◽

Gas Mixture ◽

Time Step ◽

Flow Physics ◽

Asymptotic Complexity ◽

The Continuum

AbstractIn this paper, we extend the unified gas-kinetic wave-particle (UGKWP) methods to the multi-species gas mixture and multiscale plasma transport. The construction of the scheme is based on the direct modeling on the mesh size and time step scales, and the local cell’s Knudsen number determines the flow physics. The proposed scheme has the multiscale and asymptotic complexity diminishing properties. The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale, and preserve the asymptotic Euler, Navier-Stokes, and magnetohydrodynamics (MHD) when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path. The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number. In the continuum regime, the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver. In the UGKWP, the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables, and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale. For plasma transport, the current scheme provides a smooth transition from particle-in-cell (PIC) method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime. In the continuum limit, the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time. In the highly magnetized regime, the cell size and time step are not restricted by the Debye length and plasma cyclotron period. The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.

Download Full-text