Songze Chen

Fast and accurate predictions of the spatiotemporal distributions of temperature are crucial to the multi-scale thermal management and safe operation of microelectronic devices. To realize it, an efficient semi-implicit Lax-Wendroff kinetic scheme is developed for numerically solving the transient phonon Boltzmann transport equation (BTE) from the...

Based on the unified gas kinetic scheme and discrete unified gas kinetic scheme, a concise numerical scheme is proposed to solve kinetic equation with relaxation term. The numerical scheme is shaped as a semi-implicit Richtmyer (SIR) scheme. Its interfacial flux is constructed by a finite difference solution incorporating the relaxation term which...

In this paper, a Lax–Wendroff type solver is developed to solve the governing equations for two-phase flows. By incorporating the source term into the numerical flux and approximating the cell volume force by the interfacial forces, the proposed scheme is able to restrain parasitic currents in two-phase systems. Numerical results suggest that the m...

Heat conduction in solid materials may behave like fluid dynamics when normal (N) scattering dominates phonon transport. In this hydrodynamic regime, the heat vortices have been predicted with frequency-independent relaxation time. So can this phenomena appear in other regimes? And what are the differences? In order to answer these questions, in th...

The heat transfer in solid materials at the micro- and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier’s heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find steady-state solutions to the BTE for...

Chemical vapor deposition is a method of producing thin films by chemical reactions on the substrate surface. The preparation of semiconductor devices, graphene fiber materials, carbon nanotubes, and other materials by this method involves the reaction of the rarefied gas flows. In this paper, the flow characteristics of two-component dilute gases...

Non-ideal gas flow behaviors are investigated by an Enskog-Vlasov type kinetic model considering the simultaneous effects of gas molecule size (volume exclusion) and long-range intermolecular attractions at the molecular level, which corresponds to the real gas equation of state at the macroscopic level. The Knudsen minimum is captured and a local...

In this paper, a perturbation theory of thermal rectification is developed for a thermal system where an effective thermal conductivity throughout the system can be identified and changes smoothly and slightly. This theory provides an analytical formula of the thermal rectification ratio with rigorous mathematical derivations and physical assumptio...

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...

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. {\color{red}{In this letter, a perturbation theory of thermal rectification is developed, which provides an analytical formula of the thermal rectification ratio. It reveals...

In this work, the radial thermal rectification in concentric silicon ring is studied based on the phonon Boltzmann transport equation. In the ballistic and diffusive limits, the analytical solutions reveal no thermal rectification. In the ballistic-diffusive regime, numerical results show that the thermal conductivity is a nonseparable function of...

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 th...

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 i...

Due to the presence of the steep slope and concentration of the gas distribution function in the velocity space, local velocity grid adaptation becomes necessary for high speed aerospace applications and/or other high Knudsen flow. However, the adaptation of velocity grid complicates the quadrature of discrete distribution function, degrades the ac...

This paper presents a Graphics Processing Unit (GPU) acceleration of an iteration-based discrete velocity method (DVM) for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work is based on a fast converging iterative scheme. The memory reduction techniques previously proposed for DVM are applied...

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...

An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport equation (BTE) based on the non-gray model with the consideration of phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has...

Gas-kinetic schemes (GKS) have been developed as a kinetic Finite-Volume approach to computational fluid dynamics. The GKS a priori allows to obtain approximate solutions of the fully compressible Navier-Stokes equations. In our contribution we show simulation results of compressible natural convection at large temperature differences and low Mach...

The heat transfer in solid materials at the micro-and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier's heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find the steady-state solutions of the BTE...

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...

This paper presents a Graphics Processing Units (GPUs) acceleration method of an iterative scheme for gas-kinetic model equations. Unlike the previous GPU parallelization of explicit kinetic schemes, this work features a fast converging iterative scheme. The memory reduction techniques in this method enable full three-dimensional (3D) solution of k...

An efficient implicit kinetic scheme is developed to solve the stationary phonon Boltzmann transport equation (BTE) based on the non-gray model including the phonon dispersion and polarization. Due to the wide range of the dispersed phonon mean free paths, the phonon transport under the non-gray model is essentially multiscale, and has to be solved...

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a mome...

A deterministic Boltzmann model equation solver called dugksFoam has been developed in the framework of the open source CFD toolbox OpenFOAM. The solver adopts the discrete unified gas kinetic scheme (Guo et al., 2015) with the Shakhov collision model. It has been validated by simulating several test cases covering different flow regimes including...

A memory reduction technique is proposed for solving stationary kinetic model equations. As implied by an integral solution of the stationary kinetic equation, a velocity distribution function can be reconstructed from given macroscopic variables. Based on this fact, we propose a technique to reconstruct distribution function at discrete level, and...

A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the boundaries are represented by a set of direction-oriented boundary points, and the computational grid points are classified into four different categories, the fl...

Unified gas kinetic scheme (UGKS) is an asymptotic preserving scheme for the kinetic equations. It is superior for transition flow simulations, 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 computat...

A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. The bounda...

For hypersonic flow simulation, a review of computation fluid dynamics (CFD) and a summary of gas kinetic scheme are presented in this paper. The mechanism underlying the construction of gas kinetic scheme is clarified by comparing it with the traditional CFD method. The importance of direct modeling and the implementation of the physical laws in a...

A Cartesian grid-based unified gas kinetic scheme is developed. In this approach, any oriented boundary in a Cartesian grid is represented by many directional boundary points. The numerical flux is evaluated on each boundary point. Then, a boundary flux interpolation method (BFIM) is constructed to distribute the boundary effect to the flow evoluti...

Asymptotic preserving (AP) schemes are targeting to simulate both continuum and rarefied flows. Many AP schemes have been developed and are capable of capturing the Euler limit in the continuum regime. However, to get accurate Navier-Stokes solutions is still challenging for many AP schemes. In order to distinguish the numerical effects of differen...

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S-model) are constructed for the correction of Prandtl number of the original BGK model through the modification of stress and heat flux. Even though in the continuum flow regime, both models can give the same Navier-Stokes equations with correct Prandtl number, their modification...

The dynamics of a 2D rotating Crookes radiometer is studied using a moving mesh unified gas kinetic scheme. The whole evolution process of a fan from an initial unsteady start-up to a final steady state rotational movement in a rarefied gas environment is simulated numerically. Through the numerical study, the unsteady force distribution along a va...

There is great difficulty for direct Boltzmann solvers to simulate high Knudsen number flow due to the severe steep slope and high concentration of the gas distribution function in a local particle velocity space. Local mesh adaptation becomes necessary in order to make the Boltzmann solver to be a practical tool in aerospace applications. The pres...

The present paper concerns the improvement of the gas-kinetic scheme (GKS) for low speed flow computation. In the modified GKS scheme, the flow distributions with discontinuous derivatives are used as an initial condition at the cell interface for the flux evaluation. This discontinuity is determined by considering both the flow characteristic and...

The paper introduces the gas-kinetic scheme for three-dimensional (3D) flow simulation. First, under a unified coordinate transformation, the 3D gas-kinetic BGK equation is transformed into a computational space with arbitrary mesh moving velocity. Second, based on the Chapman-Enskog expansion of the kinetic equation, a local solution of gas distri...

In this paper, a well-balanced kinetic scheme for the gas dynamic equa-tions under gravitational field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell inter-face is considered, where the amount of particle penetration and reflection is evalu-ated according to the i...

The experiment is carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we find the viscosity is important to achieve the low frequency water wave with the cooperation of hundreds of...

The experiment is carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we find the viscosity is important to achieve the low frequency water wave with the cooperation of hundreds of...