arXiv subjects

Zhaoli Guo

Publications and source records attributed to Zhaoli Guo.

At least 37 records · Page 2Linked to original sources

arXiv2022

Modified steady discrete unified gas kinetic scheme for multiscale radiative heat transfer

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than the rectangular rule used in the original SDUGKS is adopted in the proposed method in the reconstruction of energy flux across cell interface, just as the unsteady DUGKS. By this way, the characteristic line length of the modified SDUGKS establishes a relationship with the Courant-Friedrichs-Lewy (CFL) number in the DUGKS, which guarantees the accuracy of the modified SDUGKS. Furthermore, the characteristic line length is no longer limited by the extinction coefficient like in original SDUGKS. As a result, the modified SDUGKS is more accurate and robust than original SDUGKS, and more efficient than the DUGKS for steady radiation problems. Furthermore, the smooth linear interpolation and the van Leer limiter are used for problems with smooth and discontinuous optical thicknesses, respectively. Several numerical tests with optical thickness varying from optical thin to thick are conducted to validate the present scheme. Numerical results demonstrate that the modified SDUGKS can serve as an effective tool in the study of multiscale steady radiative heat transfer in participating media.

physics.comp-ph↗

arXiv2022

Central-moment discrete unified gas-kinetic scheme for incompressible two-phase flows with large density ratio

In this paper, we proposed a central moment discrete unified gas-kinetic scheme (DUGKS) for multiphase flows with large density ratio and high Reynolds number. Two sets of kinetic equations with central-moment-based multiple relaxation time collision operator are employed to approximate the incompressible Navier-Stokes equations and a conservative phase field equation for interface-capturing. In the framework of DUGKS, the first moment of the distribution function for the hydrodynamic equations is defined as velocity instead of momentum. Meanwhile, the zeroth moments of the distribution function and external force are also suitably defined such that a artificial pressure evolution equation can be recovered. Moreover, the Strang splitting technique for time integration is employed to avoid the calculation of spatial derivatives in the force term at cell faces. For the interface-capturing equation, two equivalent DUGKS methods that deal with the diffusion term differently using a source term as well as a modified equilibrium distribution function are presented. Several benchmark tests that cover a wide a range of density ratios (up to 1000) and Reynolds numbers (up to $10^5$) are subsequently carried out to demonstrate the capabilities of the proposed scheme. Numerical results are in good agreement with the reference and experimental data.

physics.flu-dyn↗

arXiv2022

Discrete unified gas kinetic scheme for the conservative Allen-Cahn equation

In this paper, the discrete unified gas kinetic scheme (DUGKS) with an improved microflux across the cell interface for the conservative Allen-Cahn equation (CACE) is proposed. In the context of DUGKS, the recovered kinetic equation from the flux evaluation with linear reconstruction in the previous DUGKS is analyzed. It is found that the calculated microflux across the cell interface is only the solution to the target kinetic equation with first order accuracy, which can result in an inaccurate CACE since the force term is involved or the first moment of the collision model has no conservation property. To correctly recover the kinetic equation up to the second order accuracy, the value of the distribution function that will propagate along the characteristic line with ending point at the cell interface is appropriated by the parabolic reconstruction instead of the linear reconstruction. To validate the accuracy of the present DUGKS for the CACE, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zaleska disk and the deformation of a circular interface, have been simulated. Numerical results show that the present DUGKS scheme is able to capture the interface with improved accuracy when compared with the previous DUGKS.

cs.CE↗

arXiv2021

On unified preserving properties of kinetic schemes

The kinetic theory provides a physical basis for developing multiscal methods for gas flows covering a wide range of flow regimes. A particular challenge for kinetic schemes is whether they can capture the correct hydrodynamic behaviors of the system in the continuum regime (i.e., as the Knudsen number $ε\ll 1$ ) without enforcing kinetic scale resolution. At the current stage, {the main approach to analyze such a property is the asymptotic preserving (AP) concept, which aims to show whether a kinetic scheme reduces to a solver for the hydrodynamic equations as $ε\to 0$, such as the shock capturing scheme for the Euler equations. However, the detailed asymptotic properties of the kinetic scheme are indistinguishable when $ε$ is small but finite under the AP framework}. In order to distinguish different characteristics of kinetic schemes, in this paper we introduce the concept of unified preserving (UP) aiming at assessing asmyptotic orders of a kinetic scheme by employing the modified equation approach and Chapman-Enskon analysis. It is shown that the UP properties of a kinetic scheme generally depend on the spatial/temporal accuracy and closely on the inter-connections among the three scales (kinetic scale, numerical scale, and hydrodynamic scale) and their corresponding coupled dynamics. Specifically, the numerical resolution and specific discretization of particle transport and collision determine the flow physics of the scheme in different regimes, especially in the near continuum limit. As two examples, the UP methodology is applied to analyze the discrete unified gas-kinetic scheme and a second-order implicit-explicit Runge-Kutta scheme in their asymptotic behaviors in the continuum limit.

math.NA↗

arXiv2021

Violation of Fourier's law in homogeneous systems

Hotspot is a ubiquitous phenomenon in microdevices/chips. In homogeneous nanoscale graphene disk with a hotspot, a graded thermal conductivity is observed previously even when the system size is fixed. However, the underlying physical mechanism is not clear. In this work, the hotspots in homogeneous 2D disk/3D ball and graphene disk are studied based on phonon Boltzmann transport equation. The mechanisms of phonon scattering are analyzed. It is found that for a system with fixed size, the graded thermal conductivity is predictable as long as there is not sufficient phonon scattering, which is independent on material properties, dimensions or system size. This work may shed light on both theoretical and experimental studies on heat dissipation of microelectronics.

cond-mat.mes-hall↗

arXiv2021

A novel transient heat conduction phenomenon to distinguish the hydrodynamic and (quasi) ballistic phonon transport

Previous studies have predicted the failure of Fourier's law of thermal conduction due to the existence of wave like propagation of heat with finite propagation speed. This non-Fourier thermal transport phenomenon can appear in both the hydrodynamic and (quasi) ballistic regimes. Hence, it is not easy to clearly distinguish these two non-Fourier regimes only by this phenomenon. In this work, the transient heat propagation in homogeneous thermal system is studied based on the phonon Boltzmann transport equation (BTE) under the Callaway model. Given a quasi-one or quasi-two (three) dimensional simulation with homogeneous environment temperature, at initial moment, a heat source is added suddenly at the center with high temperature, then the heat propagates from the center to the outer. Numerical results show that in quasi-two (three) dimensional simulations, the transient temperature will be lower than the lowest value of initial temperature in the hydrodynamic regime within a certain range of time and space. This phenomenon appears only when the normal scattering dominates heat conduction. Besides, it disappears in quasi-one dimensional simulations. Similar phenomenon is also observed in thermal systems with time varying heat source. This novel transient heat propagation phenomenon of hydrodynamic phonon transport distinguishes it well from (quasi) ballistic phonon transport.

cond-mat.mes-hall↗

arXiv2020

On the formulations of interfacial force in the phase-field-based lattice Boltzmann method

Different formulations of interfacial force have been adopted in phase-field-based lattice Boltzmann method for two-phase flows. Although they are identical mathematically, their numerical performances may be different due to truncation errors in the discretization. In this paper, four-type formulations of interfacial force available in the literature, namely stress tensor form (STF), chemical potential form (CPF), pressure form (PF) and continuum surface force (CSF) form, are compared and discussed. A series of benchmark problems, including stationary droplet, two merging droplets, Capillary wave, rising bubble and drop deformation in shear flow, are simulated. Numerical results show that CPF is a good choice for small surface deformation problems while STF is preferred for dynamical problems, both STF and CSF demonstrate good numerical stability.

physics.flu-dyn↗

arXiv2020

Well-balanced lattice Boltzmann equation for two-phase flows

The standard lattice Boltzmann equation (LBE) method usually fails to capture the physical equilibrium state of a two-phase fluid system, i.e., zero velocity and constant chemical potential. Consequently, spurious velocities and inconsistent thermodynamic density properties are frequently encountered in LBE simulations. In this work, based on a rigorous analysis of the discrete balance equation of LBE, we identify the structure of the force imbalance due to discretization errors from different parts. Then a well-balanced LBE is proposed which can achieve the discrete equilibrium state. The well-balanced properties of the LBE are confirmed by some numerical tests of a flat interface problem and a droplet system.

physics.flu-dyn↗

arXiv2020

Heat vortexes of ballistic, diffusive and hydrodynamic phonon transport in two-dimensional materials

In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As long as there is not sufficient R scattering, the heat vortexes can appear in present simulations.

cond-mat.mes-hall↗

arXiv2020

Perturbation theory of thermal rectification

Thermal rectification which is a diode-like behavior of heat flux has been studied over a long time. However, a universal and systematic physical description is still lacking. In this letter, a perturbation theory of thermal rectification is developed, which provides an analytical formula of the thermal rectification ratio. It reveals the linear relationship between the thermal rectification ratio and temperature difference. Furthermore, the size-dependence of the thermal rectification relies on the specific form of the thermal conductivity. In addition, several experimental and numerical observations in previous literatures are well explained. This theory can be applicable to any system in which a differentiable effective thermal conductivity can be derived, and is helpful to unveil general principle for thermal rectification.

cond-mat.mes-hall↗

arXiv2020

Non-ideal gas dynamics under confinement: rarefaction effect, dense effect and molecular interaction

The effects of volume exclusion and long-range intermolecular attraction are investigated by the simplified kinetic model for surface-confined inhomogeneous fluids. Gas dynamics of the ideal gas, the hard-sphere fluid and the real gas are simulated by the Boltzmann equation, the Enskog equation and the simple kinetic equation, respectively. Only the Knudsen minimum appears for the ideal gas, while both the Knudsen minimum and the Knudsen maximum occur for the hard-sphere fluid and the real gas under certain confinements, beyond which the maximum and minimum may disappear. The Boltzmann equation and the Enskog equation overestimates and underestimates the mass flow rate of the real gas dynamics under confinement, respectively, where the volume exclusion and the long-range intermolecular attractive potential among molecules are not ignorable. With the increase of the channel width, gas dynamics of the hard-sphere fluid and the real gas tends to the Boltzmann prediction gradually. The density inhomogeneity, which hinders the flow under confinement, is more obvious when the solid fraction is larger. The anomalous slip occurs for real gas under constant confinement. The flow at a smaller Knudsen number (larger solid fraction or channel width) contributes more practical amount of mass transfer, although the rarefaction effects is more prominent at larger Knudsen numbers. The temperature has no effect on density and velocity profiles of the ideal gas and the hard-sphere fluid, but the energy parameter among the real gas molecules decreases with the increasing temperature and the real gas dynamics tends to the hard-sphere ones consequently.

physics.flu-dyn↗

arXiv2020

Non-equilibrium transport of inhomogeneous shale gas under ultra-tight confinement

The non-equilibrium transport of inhomogeneous and dense gases highly confined by surface is encountered in many engineering applications. For example, in the shale gas production process, methane is extracted from ultra-tight pores under high pressure so the gas is inhomogeneous and dense. Currently, the complex non-equilibrium transport of inhomogeneous and dense gases where gas surface interactions play a key role is commonly investigated by molecular dynamics or on a continuum-assumption basis. Here, a tractable kinetic model based on the generalized Enskog equation and the mean-field theory is employed to couple the effects of the volume exclusion and the long-range intermolecular attraction forces. The interactions between gas molecules and confined surface are modelled by a 10-4-3 Lennard-Jones potential, which can capture gas surface adsorption. The cross-sectional density profiles of methane under different confinements are in good agreement with the molecular dynamics results reported in the literature, and the transport behaviors are validated by the non-equilibrium molecular dynamics. The velocity of methane flow in shale matrix is plug-like due to its dense characteristics in nanopores. The influence of pressure, temperature, pore size and shale composition on density and velocity profiles is analyzed quantitatively. Our results show that the Klinkenberg correction is not applicable to model shale gas flow in the production process; the Navier-Stokes model using the second-order slip boundary condition cannot produce the proper velocity profiles, and consequently fails to predict the accurate flow rate in nanopores. This study sheds new light on understanding the physics of non-equilibrium dense gas flows in shale strata.

physics.geo-ph↗

arXiv2019

Radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime

The radial thermal rectification in the concentric silicon ring from ballistic to diffusive regime is investigated based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions prove that there is no thermal rectification. In the ballistic-diffusive regime, the heat flux prefers to flow from the inner boundary to the outer boundary. Furthermore, as the characteristic length (the distance between two circular boundaries) increases from tens of nanometers to tens of microns, the thermal rectification ratio enhances first and then fades away gradually. It attributes to that as the direction of the temperature gradient changes, the average phonon mean free path changes. The difference of the average phonon mean free path finally leads to the change of the heat flux or thermal conductivity. As the temperature decreases, the maximum thermal rectification ratio decreases. In addition, as the radius ratio between the inner and outer boundary increases, the thermal rectification ratio decreases for a given characteristic length.

cond-mat.mes-hall↗

arXiv2019

Spontaneous shrinkage of droplet on wetting surface in phase-field model

Phase field theory is widely used to model multi-phase flows. A drop can shrink or grow spontaneously due to the redistribution of interface and bulk energies to minimize the system energy. In this paper, the spontaneous behaviour of a drop on a flat surface is investigated. It is found that there exists a critical radius dependent on the contact angle, the domain size and the interface width, below which the droplet will eventually disappear. In particular, the critical radius can be very large when the contact angle is hydrophilic. The theoretical prediction of the critical radius is verified numerically by simulating a drop on a surface with various contact angles, the domain sizes and the interface widths.

physics.flu-dyn↗

arXiv2019

Local reactive boundary scheme for lattice Boltzmann method

In this paper, a boundary scheme is proposed for the two-dimensional five-velocity (D2Q5) lattice Boltzmann method with heterogeneous surface reaction, in which the unknown distribution function is determined locally based on the kinetic flux of the incident particles. Compared with previous boundary schemes, the proposed scheme has a clear physical picture that reflects the consumption and production in the reaction. Furthermore, the scheme only involves local information of boundary nodes such that it can be easily applied to complex geometric structures. In order to validate the accuracy of the scheme, some benchmark tests, including the convection-diffusion problems in straight and inclined channels are conducted. Numerical results are in excellent agreement with the analytical solutions, and the convergence tests demonstrate that second-order spatial accuracy is achieved for straight walls, and the order of accuracy is between 1.5 and 2.0 for general inclined walls. Finally, we simulated the density driving flow with dissolution reactions in a two-dimensional cylindrical array, and the results agree well with those in previous studies

physics.comp-ph↗

arXiv2019

A well-balanced gas kinetic scheme for Navier-Stokes equations with gravitational potential

The hydrostatic equilibrium state is the consequence of the exact hydrostatic balance between hydrostatic pressure and external force. Standard finite volume or finite difference schemes cannot keep this balance exactly due to their unbalanced truncation errors. In this study, we introduce an auxiliary variable which becomes constant at isothermal hydrostatic equilibrium state and propose a well-balanced gas kinetic scheme for the Navier-Stokes equations with a global reconstruction. Through reformulating the convection term and the force term via the auxiliary variable, zero numerical flux and zero numerical source term are enforced at the hydrostatic equilibrium state instead of the balance between hydrostatic pressure and external force. Several problems are tested numerically to demonstrate the accuracy and the stability of the new scheme, and the results confirm that, the new scheme can preserve the exact hydrostatic solution. The small perturbation riding on hydrostatic equilibria can be calculated accurately. The viscous effect is also illustrated through the propagation of small perturbation and the Rayleigh-Taylor instability. More importantly, the new scheme is capable of simulating the process of converging towards hydrostatic equilibrium state from a highly non-balanced initial condition. The ultimate state of zero velocity and constant temperature is achieved up to machine accuracy. As demonstrated by the numerical experiments, the current scheme is very suitable for small amplitude perturbation and long time running under gravitational potential.

physics.flu-dyn↗

arXiv2018

A fast synthetic iterative scheme for the stationary phonon Boltzmann transport equation

In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic diffusion equation for the temperature, which is obtained from the zero- and first-order moment equations of the phonon BTE. The synthetic diffusion equation, which is asymptomatically preserving to the Fourier's heat conduction equation in the diffusive regime, contains a term related to the Fourier's law and a term determined by the second-order moment of the distribution function that reflects the non-Fourier heat transfer. The mesoscopic kinetic equation and macroscopic diffusion equations are tightly coupled together, because the diffusion equation provides the temperature for the BTE, while the BTE provides the high-order moment to the diffusion equation to describe the non-Fourier heat transfer. This synthetic iterative scheme strengthens the coupling of all phonons in the phase space to facilitate the fast convergence from the diffusive to ballistic regimes. Typical numerical tests in one-, two-, and three-dimensional problems demonstrate that our scheme can describe the multiscale heat transfer problems accurately and efficiently. For all test cases convergence is reached within one hundred iteration steps, which is one to three orders of magnitude faster than the traditional implicit DOM in the near-diffusive regime.

physics.comp-ph↗

arXiv2018

A fractional step lattice Boltzmann model for two phase flows with large density differences

In this paper, a fractional step lattice Boltzmann method is proposed to model two-phase flows with large density differences by solving Cahn-Hilliard phase-field equation and the incompressible Navier-Stokes equations.In order to maintain a hyperbolic tangent property of the interface profile and conserve the volume, an interfacial profile correction term and a flux correction term are added into the original Cahn-Hilliard equation respectively. By using a fractional step scheme, the modified Cahn-Hilliard equation is split into two sub-equations. One is solved in the framework of lattice Boltzmann equation method. The other is solved by the finite difference method. Compared with the previous lattice Boltzmann methods, the proposed method is able to maintain the order parameter within a physically meaningful range, which is conductive to track the interface accurately. In addition, the multi-relaxation-time collision model and a high-order compact selective filter operation are employed to enhance the numerical stability. The proposed method can simulate two-phase fluid flows with the density ratio up to $1000$. In order to validate the accuracy and capability of the method, several benchmark problems, including single vortex deform of a circle, translation of a drop, Laplace-Young law, capillary wave and rising bubble with large density ratios, are presented. The results are in good agreement with the analytical solutions and the data in the literature for the investigated benchmarks.

physics.flu-dyn↗