Unified Gas Kinetic Scheme Research Articles

Multiscale Simulation for the System of Radiation Hydrodynamics

This paper aims at the simulation of multiple scale physics for the system of radiation hydrodynamics. The system couples the fluid dynamic equations with the radiative heat transfer. The coupled system is solved by the gas-kinetic scheme (GKS) for the compressible inviscid Euler flow and the unified gas-kinetic scheme (UGKS) for the non-equilibrium radiative transfer, together with the momentum and energy exchange between these two phases. For the radiative transfer, due to the possible large variation of fluid opacity in different regions, the transport of photons through the flow system is simulated by the multiscale UGKS, which is capable of naturally capturing the transport process from the photon’s free streaming to the diffusive wave propagation. Since both GKS and UGKS are finite volume methods, all unknowns are defined inside each control volume and are discretized consistently in the updates of hydrodynamic and radiative variables. For the coupled system, the scheme has the asymptotic preserving property, such as recovering the equilibrium diffusion limit for the radiation hydrodynamic system in the optically thick region, where the cell size is not limited by photon’s mean free path. A few test cases, such as radiative shock wave problems, are used to validate the current approach.

The UGKS Simulation of Microchannel Gas Flow and Heat Transfer Confined Between Isothermal and Nonisothermal Parallel Plates

Abstract The unified gas kinetic scheme (UGKS) is introduced to simulate the near transition regime gas flow and heat transfer in microchannel confined between isothermal and nonisothermal parallel plates. The argon gas is used and its inlet Knudsen number (Knin) ranges from 0.0154 to 0.0715. It is found that: (1) both microchannel gas flows under isothermal and nonisothermal parallel plates display a trend of speed acceleration and temperature decrease along flow direction, for which the microscopic mechanism explanation is first proposed; (2) inlet gas streamlines under nonisothermal plates condition deviate from the parallel distributions under isothermal plates condition due to the dual driving effects of pressure drop along flow direction and temperature difference along cross section; (3) gas temperature, pressure, density and viscosity distributions along cross section under nonisothermal plates condition deviate from the parabolic distributions under isothermal plates condition, while the gas velocity keeps the parabolic distribution due to the effect of Knudsen layer; (4) as channel height increases or channel length and gas molecular mean free path decrease, the gas temperature distribution along cross section under nonisothermal plates condition tends to transition from linear to curve one due to the decreasing effect of heat transfer along cross section and increasing effect of gas acceleration along flow direction, this transition from linear to curve one becomes more obvious along flow direction. (5) the gas velocity under nonisothermal plates condition decreases with the increase of inlet gas temperature (Tin), lower plate temperature (Tl) and Knin, while the gas temperature increases with the increase of Tin, Tl and Knin.

Numerical analysis of nonlinear thermal stress flow between concentric elliptical cylinders

The present study numerically investigates nonlinear thermal stress in a rarefied gas flow between two coaxial elliptic cylinders with a hot outer wall. Monatomic argon is considered, and isothermal boundary conditions are implemented on the walls. Three different numerical methods are used to solve this problem, i.e., first, the direct simulation Monte Carlo (DSMC) method is used and validated against the numerical solution of the Boltzmann equation available in the literature. The results of the DSMC algorithm are compared with the results of the discrete unified gas kinetic scheme and the continuum set of equations of slow non-isothermal flows, which includes nonlinear thermal stress terms compared to the Navier–Stokes equations. For the first time, the flow is examined in a wide range of Knudsen numbers in the slip regime from the Knudsen number (Kn) of Kn = 0.005 to Kn = 0.1. At a minimal Knudsen number, there is just one vortex due to the nonlinear thermal stress flow; however, as Kn increases, the velocity peak near the inner cylinder is replaced with another vortex, which is created due to the second-order thermal creep effects on the inner wall of the cylinder. We show that as Kn increases, the inner vortex increases in size, while the outer vortex shrinks. The mechanisms of the formation of both vortices are described in detail. Other flow characteristics, including walls’ velocity slip, shear stress, and vorticity, are discussed.

Multiscale kinetic inviscid flux extracted from a gas-kinetic scheme for simulating incompressible and compressible flows.

A kinetic inviscid flux (KIF) is proposed for simulating incompressible and compressible flows. It is constructed based on the direct modeling of multiscale flow behaviors, which is used in the gas-kinetic scheme (GKS), the unified gas-kinetic scheme (UGKS), the discrete unified gas-kinetic scheme (DUGKS), etc. In KIF, the discontinuities (such as the shock wave) that cannot be well resolved by mesh cells are mainly solved by the kinetic flux vector splitting (KFVS) method representing the free transport mechanism (or microscale mechanism), while in other flow regions that are smooth, the flow behavior is solved mainly by the central-scheme-like totally thermalized transport (TTT). The weights of KFVS and TTT in KIF is automatically determined by those in the theory of direct modeling. Two ways of choosing the weights in KIF are proposed, which are actually the weights adopted in the UGKS and the DUGKS, respectively. By using the test cases of the Sod shock tube, the rarefaction wave, the boundary layer of a flat plate, the cavity flow, hypersonic flow over a circular cylinder, the shock and turbulent boundary iteration, and transonic flow over a three-dimensional M6 wing, the validity and accuracy of the present method are examined. The KIF does not suffer from the carbuncle phenomenon, and does not introduce extra numerical viscosity in smooth regions. Especially in the case of hypersonic cylinder, it gives quite sharp and clear density and temperature contours. The KIF can be viewed as an inviscid-viscous splitting version of the GKS. By doing this splitting, it is easy to be used in traditional computational fluid dynamics frameworks. It can also be classified as a type in the numerical schemes based on the kinetic theory that are represented by the works of Sun etal. [Adv. Appl. Math. Mech. 8, 703 (2016)10.4208/aamm.2015.m1071] and Ohwada etal. [J. Comput. Phys. 362, 131 (2018)JCTPAH0021-999110.1016/j.jcp.2018.02.019], except the weights are determined by the weights of direct modeling.

A unified gas-kinetic scheme for micro flow simulation based on linearized kinetic equation

The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number Kn, which is defined as the ratio of the mean free path over the local characteristic length. On the kinetic scale, the dynamics of a small-perturbed micro flow can be described by the linearized kinetic equation. In the continuum regime, according to the Chapman-Enskog theory, hydrodynamic equations such as linearized Euler equations and Navier-Stokes equations can be derived from the linearized kinetic equation. In this paper, we are going to propose a unified gas kinetic scheme (UGKS) based on the linearized kinetic equation. For the simulation of small-perturbed micro flow, the linearized scheme is more efficient than the nonlinear one. In the continuum regime, the cell size and time step of UGKS are not restricted to be less than the particle mean free path and collision time, and the UGKS becomes much more efficient than the traditional upwind-flux-based operator-splitting kinetic solvers. The important methodology of UGKS is the following. Firstly, the evolution of microscopic distribution function is coupled with the evolution of macroscopic flow quantities. Secondly, the numerical flux of UGKS is constructed based on the integral solution of kinetic equation, which provides a genuinely multiscale and multidimensional numerical flux. The UGKS recovers the solution of linear kinetic equation in the rarefied regime, and converges to the solution of the linear hydrodynamic equations in the continuum regime. An outstanding feature of UGKS is its capability of capturing the accurate viscous solution in bulk flow region once the hydrodynamic flow structure can be resolved by the cell size even when the cell size is much larger than the kinetic length scale, such as the capturing of the viscous boundary layer with a cell size being much larger than the particle mean free path. Such a multiscale property is called unified preserving (UP) which has been studied in (Guo, et al. arXiv preprint arXiv:1909.04923, 2019). In this paper, a mathematical proof of the UP property for UGKS will be presented and this property is applicable to UGKS for solving both linear and nonlinear kinetic equations.

A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on a three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Based on the direct modeling methodology, the unified gas-kinetic scheme (UGKS) models the flow dynamics directly on the numerical mesh size and time step scales, and it is able to capture the flow dynamics from the kinetic scale particle transport to the hydrodynamic wave propagation seamlessly according to the local cell Knudsen number. Instead of discretizing the particle velocity space in UGKS, the UGKWP method is composed of evolution of deterministic wave and stochastic particles. With dynamic wave-particle decomposition according to the cell Knudsen number, the UGKWP method is able to capture the continuum wave interaction and rarefied particle transport under a unified framework and achieves high efficiency in different flow regimes. The UGKWP flow solver is constructed in three-dimensional space and is validated by many test cases at different Mach and Knudsen numbers. The examples include a 3D shock tube problem, lid-driven cubic cavity flow, high-speed flow passing through a cubic object, and hypersonic flow around a space vehicle. The parallel performance has been tested on the Tianhe-2 supercomputer, and reasonable parallel performance has been observed up to 1000 cores. With the wave-particle formulation, the UGKWP method has great potential in solving three-dimensional multiscale transport problems with the co-existence of continuum and rarefied flow regimes, especially for the high-speed rarefied and continuum flow simulation around a space vehicle in near-space flight, where the local Knudsen number can vary significantly with five or six orders of magnitude differences.

A simplified discrete unified gas kinetic scheme for incompressible flow

The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows, which combines the benefits of both the lattice Boltzmann method and UGKS. By the reconstruction of the gas distribution function using particle velocity characteristic lines, the flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with the reconstruction stage on a whole time step instead of a half time step in the original DUGKS. Using the temporal/spatial integral Boltzmann Bhatnagar–Gross–Krook equation, the auxiliary distribution function with the inclusion of the collision effect is adopted. The macroscopic and mesoscopic fluxes of the cell on the next time step are predicted by the reconstruction of the auxiliary distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on the next time step can be updated through its flux, which is a moment of the predicted mesoscopic flux at cell interfaces. The equilibrium distribution function on the next time step can also be updated. The gas distribution function is updated by the FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. The numerical time step is only limited by the Courant–Friedrichs–Lewy condition, and a relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, and microcavity flow cases, are conducted to validate the present scheme. The observed numerical simulation results reasonably agree with the reported results.

A ghost-cell discrete unified gas kinetic scheme for thermal flows with heat flux at curved interface

The discrete unified gas kinetic scheme (DUGKS) is advanced for simulating thermal convections with curved heat flux condition using the ghost-cell (GC) approach. The fluid flow and temperature field combined under the Boussinesq approximation are solved by the double-population model. The ghost-cell immersed boundary method is applied to the curved heat-flux interface, where fictitious cells are set in the solid domain. The information at the centers of those cells is extrapolated from the fluid-solid interface and the neighboring flow. The heat-flux boundary condition at the interface can then be incorporated into the solution of the entire thermal flow. Note that the extrapolation/interpolation involved in the GC-DUGKS is accomplished through a sharp interface manner. Therefore, the difficulty in handling the heat-flux boundary condition for the diffuse-type immersed boundary methods due to the cross contamination is removed. Furthermore, the thermal buoyancy force is conveniently combined with the governing equation by the Strang-splitting scheme. Simulations of several well-established convection-diffusion flow problems with heat flux at the curved interface are performed to validate the present GC-DUGKS. The results demonstrate the accuracy and feasibility of the method.

Discrete unified gas kinetic scheme for steady multiscale neutron transport

A discrete unified gas kinetic schemes (DUGKS) is developed to solve the steady multidimensional and multigroup neutron transport problems based on the Boltzmann equation. Compared with the traditional neutron transport methods, this steady DUGKS (SDUGKS) has the asymptotic preserving properties and can give good numerical predictions for multiscale transport ranging from optically thin to optically thick regimes (diffusive limit). In the SDUGKS a delta-form-based discrete ordinate (SN) framework is adopted to solve the steady Boltzmann transport equation. But unlike the direct interpolation in the traditional numerical methods for neutron transport, the interface angular fluxes are obtained by integrating the steady Boltzmann equation along the neutron transport direction. The traditional step schemes or other robust schemes can be adopted to discretize the increment to ensure numerical stability. Based on the above special treatments, the sweeping and iterative strategies of the new developed SDUGKS are completely the same as those of the traditional steady SN methods, and thus SDUGKS can be easily implemented in the existing SN transport codes, only by adding the residuals into the source terms. Several numerical tests are performed and the numerical solutions show that the results of the present SDUGKS agree well with the reference solutions for problems with different values of optical thickness, which indicates the advantages of the developed SDUGKS over the conventional methods. Overall, the SDUGKS can serve as a potential numerical tool for multiscale neutron transport problems covering a wide range of optical thickness.

A multi-prediction implicit scheme for steady state solutions of gas flow in all flow regimes

An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell interface, a numerical flux with construction similar to discrete unified gas-kinetic scheme (DUGKS) is applied to ensure multiscale property and make the scheme free from the influence of cell Knudsen number. The idea of the macroscopic variable prediction is adopted and further developed to form an efficient implicit method, where a second order prediction scheme based on the Navier-Stokes (NS) equation is constructed to predict macroscopic variables from macroscopic residuals for the microscopic implicit system, and then a multiple prediction structure is formed. The accurate prediction procedure endows the implicit numerical system with high convergence speed in all flow regimes, especially in the continuum flow regime where NS solution is directly predicted and the convergence is accelerated greatly. Test cases show that the present method is accurate and efficient, and is one order of magnitude faster than the previous prediction-based implicit multiscale scheme in the continuum flow regime.

A novel multiscale discrete velocity method for model kinetic equations

This paper focuses on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methodsrepresented by unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved.

Reduced order modeling-based discrete unified gas kinetic scheme for rarefied gas flows

Boltzmann solvers face significant difficulty in simulating rarefied flows at high Knudsen numbers. In this flow regime, the gas distribution function is widely scattered and highly concentrated with a very steep slope in the particle velocity space. In order to capture the feature of such a flow, the Boltzmann solvers such as the Discrete Unified Gas Kinetic Scheme (DUGKS) discretize the particle velocity space with a very fine mesh (many discrete particle velocities) using the Discrete Velocity Method (DVM) due to which the load for computation becomes unendurable. In this paper, a Reduced Order Modeling (ROM) method is used to generate a reduced discrete velocity space for the DUGKS. More specifically, the discrete empirical interpolation method [S. Chaturantabut and D. C. Sorensen, SIAM J. Sci. Comput. 32, 2737–2764 (2010)] is used to select the dominant nodes in the original discrete velocity space to form a reduced discrete velocity space, which represents important dynamical characteristics. In this way, most grid points in the discrete velocity space, which are of negligible importance on the integration, are removed in practical computation, which yields a significant improvement in computational efficiency. The proposed ROM approach is not limited to a specific DVM-based solver. For illustration, in this paper, we developed the Reduced Order Modeling-based Discrete Unified Gas Kinetic Scheme (ROM-DUGKS) by applying the reduced velocity space to the conventional DUGKS. Validations are performed in both low-speed and hypersonic rarefied flows at various Knudsen numbers. The results show that the ROM-DUGKS is much more efficient than the original DUGKS while still maintaining high accuracy. This significant improvement in computational efficiency will unleash the potential of the DVM-based solvers such as the DUGKS for practical applications to rarefied flow problems.

Discrete unified gas kinetic scheme for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes

In this paper, the discrete unified gas kinetic scheme (DUGKS), which is a novel direct kinetic method, is developed for a reformulated BGK–Vlasov–Poisson system in all electrostatic plasma regimes characterized by a wide range of Knudsen number and normalized Debye length. The current scheme is constructed for multiscale plasma simulation, while the temporal and spatial step sizes of the method are not restricted by the Knudsen number and normalized Debye length. One key feature of this method is the un-splitting treatment of the particle transport, collision and acceleration in both the distribution function evolution and the numerical flux evaluation, which enables the method to economically and accurately provide a satisfactory solution for all Knudsen number regimes. With the coupling of the appropriate time discretization of the distribution function and a reformulated Poisson equation, the method further provides an easy-to-implement and efficient way for the investigation of electrical potential in all normalized Debye regimes. As a result, the proposed DUGKS becomes an asymptotic preserving scheme, which automatically degenerates to be consistent with the discretization of corresponding limiting models. Several numerical experiments in different electrostatic plasma regimes are presented to validate the proposed method.

A velocity-space adaptive unified gas kinetic scheme for continuum and rarefied flows

Compressible flow has intrinsically multiple scale nature due to the large variations of gas density and characteristic scale of flow structure, especially in hypersonic and reentry problems. It is challenging to construct an accurate and efficient numerical algorithm to capture non-equilibrium flow physics across different regimes. In this paper, a unified gas kinetic scheme with adaptive velocity space (AUGKS) for multiscale flow transport will be developed. In near-equilibrium flow region, particle distribution function is close to the Chapman-Enskog expansion and can be formulated analytically, where only macroscopic conservative flow variables are updated. With the emergence of non-equilibrium effect, the AUGKS automatically switches to the original unified gas kinetic scheme (UGKS) with a discrete velocity space to follow the evolution of particle distribution function. A criterion is proposed to quantify the non-equilibrium and is used for the switch between continuous and discrete particle velocity space. Following the scale-dependent local evolving solution, the AUGKS presents the discretized gas dynamic equations directly on the cell size and time step scales, i.e., the so-called direct modeling method. As a result, the scheme is able to capture the cross-scale flow physics from particle transport to hydrodynamic wave propagation, and provides a continuous variation of solutions from the Boltzmann to the Euler equations. Different from conventional DSMC-Fluid hybrid method, the AUGKS does not need a buffer zone to match up kinetic and hydrodynamic solutions. Instead, continuous and discrete particle velocity spaces are automatically and robustly switched, such as translating the continuous Chapman-Enskog distribution function to the discrete grid points in the velocity space. Therefore, the AUGKS is feasible for the numerical simulations with unsteadiness and complex geometries. Compared with the asymptotic preserving (AP) method which solves kinetic equation uniformly over entire computational domain with discretized velocity space, the current velocity-space adaptive unified scheme speeds up the computation, reduces the memory requirement significantly, and maintains the equivalent accuracy for multiscale flow simulations. Many test cases validate the current approach. The AUGKS provides an effective tool for non-equilibrium flow studies.

Discrete unified gas kinetic scheme for electrostatic plasma and its comparison with the particle-in-cell method.

In this paper, we present a finite-volume direct kinetic method, the so-called discrete unified gas kinetic scheme (DUGKS), for electrostatic plasma. One key feature of this method is the semi-implicit unsplitting treatment of particle transport and collision, and thus the time step in current DUGKS is not limited by the particle collision time. In addition, a fourth-order compact MUSCL scheme with a positivity preserving limiter is implemented in the interface reconstruction, which enables present DUGKS to preserve the favorable conservative property and positivity of distribution function. Combined with this MUSCL method, the semi-Lagrangian scheme is used for the particle transport in velocity space to remove Courant-Friedricks-Lewy restriction induced by the large electric force. As a result, the proposed DUGKS becomes an efficient and stable multiscale scheme. Several numerical experiments, including plasma sheath, linear Landau damping, collisional nonlinear Landau damping, and plasma ion acceleration, are performed to validate current DUGKS. A comparative study of current DUGKS with a general particle in cell (PIC) method which could handle particle collision in a conservative way is also presented. Theory and numerical experiments demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes, while the PIC method is desired for the field- dominated plasma flows involving a wide range of velocities.

Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids.

This work is an extension of the discrete unified gas kinetic scheme (DUGKS) from rarefied gas dynamics to strongly inhomogeneous dense fluid systems. The fluid molecular size can be ignored for dilute gases, while the nonlocal intermolecular collisions and the competition of solid-fluid and fluid-fluid interactions play an important role for surface-confined fluid flows at the nanometer scale. The nonequilibrium state induces strong fluid structural-confined inhomogeneity and anomalous fluid flow dynamics. According to the previous kinetic model [Guo etal., Phys. Rev. E 71, 035301(R) (2005)10.1103/PhysRevE.71.035301], the long-range intermolecular attraction is modeled by the mean-field approximation, and the volume exclusion effect is considered by the hard-sphere potential in the collision operator. The kinetic model is solved by the DUGKS, which has the characteristics of asymptotic preserving, low dissipation, second-order accuracy, and multidimensional nature. Both static fluid structure and dynamic flow behaviors are calculated and validated with Monte Carlo or molecular dynamics results. It is shown that the flow of dense fluid systems tends to that of rarefied gases as the dense degree decreases or the mean flow path increases. The DUGKS is proved to be applicable to simulate such nonequilibrium dense fluid systems.

Analysis and assessment of the no-slip and slip boundary conditions for the discrete unified gas kinetic scheme.

The discrete unified gas kinetic scheme (DUGKS) with a force term is a finite volume solver for the Boltzmann equation. Unlike the standard lattice Boltzmann method (LBM), DUGKS can be applied on nonuniform grids. For both the LBM and DUGKS, the boundary conditions need to be processed through the density distribution function. So researchers introduced the boundary conditions from the LBM frame into the DUGKS. However, the accuracy of these boundary conditions in the DUGKS has not been studied thoroughly. Through strict theoretical deduction, we find that the bounce-back (BB) scheme leads to a different dependence of the numerical error term in the DUGKS as compared to the LBM. The error term is influenced by the relaxation time and the body force. And it can be reduced by lowering the kinetic viscosity. Unlike the BB scheme, the nonequilibrium bounce-back scheme has the ability to implement real no-slip boundary condition. Furthermore, two slip boundary conditions incorporated with Navier's slip model are introduced from the LBM framework into the DUGKS. The tangential momentum change-based (TMAC) scheme can be used directly in the DUGKS because it generates no numerical error term in the DUGKS. For the combination of the bounce-back and specular reflection schemes (BSR), the relation between the slip length and the combination parameter should be modified in accordance with the numerical error term. Analysis shows that the TMAC scheme can simulate a wider range of slip length than the BSR scheme. Numerical simulations of the Couette flow and the Poiseuille flow confirm our theoretical analysis.

Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations.

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for a general nonlinear convection-diffusion equation (NCDE) and show that the NCDE can be recovered correctly from the present model through the Chapman-Enskog analysis. We then test the present DUGKS through some classic convection-diffusion equations, and we find that the numerical results are in good agreement with analytical solutions and that the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, the DUGKS can also adopt the nonuniform mesh. Besides, we perform some comparisons among the DUGKS, the finite-volume lattice Boltzmann model (FV-LBM), the single-relaxation-time lattice Boltzmann model (SLBM), and the multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the present DUGKS is more accurate than the FV-LBM, more stable than the SLBM, and almost has the same accuracy as the MRT-LBM. Moreover, the use of nonuniform mesh may make the DUGKS model more flexible.

Unified gas-kinetic wave-particle methods III: Multiscale photon transport

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to multiscale photon transport. In this method, the photon free streaming and scattering processes are treated in an un-splitting way. The photon distribution is described by both discrete simulation particle and analytic distribution function. By accurately recovering the multiscale modeling of the unified gas-kinetic scheme (UGKS), the UGKWP method presents a smooth transition for photon transport from optically thin to optically thick regimes according to the cell's Knudsen number. In the optically thin regime, the UGKWP method performs as a Monte Carlo type particle tracking method, while in the optically thick regime it recovers a diffusion process without particles. The proportion of wave-described and particle-described photons is automatically adapted according to the numerical resolution and local photon scattering physics, i.e., the so-called cell Knudsen number. Compared to the discrete ordinates-based UGKS, the UGKWP method requires less memory and does not suffer from ray effect. Compared to the implicit Monte Carlo (IMC) method, the statistical noise of the UGKWP method is greatly reduced, and the computational efficiency is significantly improved in the optically thick regime. Several numerical examples covering all transport regimes from the optically thin to optically thick ones are computed to validate the accuracy and efficiency of the UGKWP method. In comparison with the UGKS and IMC method, the UGKWP method may have a several-order-of-magnitude reduction in computational cost and memory requirement in solving some multiscale transport problems.

Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer

In 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.