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 Lattice Boltzmann Method (LBM) and unified gas kinetic scheme (UGKS). By reconstruction of gas distribution function using particle velocity characteristic line, flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with reconstruction stage on a whole time step instead of half time step in original DUGKS. Using temporal/spatial integral Boltzmann Bhatnagar-Gross-Krook (BGK) equation, the transformed distribution function with inclusion of collision effect is constructed. The macro and mesoscopic fluxes of the cell on next time step is predicted by reconstruction of transformed distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on next time step can be updated through its macroscopic flux. Equilibrium distribution function on next time step can also be updated. Gas distribution function is updated by 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. Numerical time step is only limited by the Courant-Friedrichs-Lewy (CFL) condition and 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, as well as micro cavity flow cases are conducted to validate present scheme. The numerical simulation results agree well with the references' results.
Fokker-Planck Kinetic description of small-scale fluid turbulence for classical incompressible fluids
扩展的统计方法提出了一个平行的文件\cite % {Tessarotto 2008-aa}，这项工作的目的是提出一个随机逆动力学理论的基础上引入一个合适的\textit{local phase-space probability density function}（pdf）的小尺度流体动力学湍流。特别是，我们提出的问题的建设福克-普朗克动力学模型的水动力湍流。这里采用的方法是基于所谓的IKT方法（逆动力学理论），由Ellero等人（2004-2008）开发的，其允许基于采用局部pdf的不可压缩流体的精确相空间描述。我们打算表明，对于规定的随机模型，本方法允许确定唯一的随机流体场的时间演化。随机平均的本地PDF服从动力学方程，虽然一般非马尔可夫，局部速度空间中可以近似通过一个合适的福克-普朗克动力学方程。作为副作用，相同的pdf被证明通常具有非高斯行为。
A discrete unified gas-kinetic scheme for immiscible two-phase flows
在这项工作中，我们扩展了离散统一气体动力学方案（DUGKS）[Guo et al.，E88，033305（2013）]以继续两相流。在DUGKS框架中，使用两个动力学模型方程来求解准不可压缩相场控制方程[Yang et al.，E 93，043303（2016）]。一个是Chan-Hilliard（CH）方程，另一个是纳维-斯托克斯方程。通过Chapman-Enskog分析，DUGKS方法可以正确地恢复准不可压缩相场控制方程。与以前的基于相场的LB模型不同，DUGKS中的Courant-Friedricks-Lewy条件是可调的，这可以增加数值稳定性。此外，有限体积公式可以很容易地实现非均匀网格，可以提高数值精度的模型。通过模拟静止液滴、分层Poiffille流、上升气泡和Rayleigh-Taylor不稳定性，并与准不可压格子玻尔兹曼方法（LBM）进行比较，验证了该模型的有效性。数值计算结果表明，该方法能够高精度、稳定地跟踪界面。该模型也能够处理更广泛的粘度和密度比的准不可压缩格子玻尔兹曼模型。该模型是一种很有前途的两相流数值模拟工具。
Kinetic modeling of multiphase flow based on simplified Enskog equation
在离散Boltzmann方法（DBM）的框架下，提出了一种新的多相流动力学模型。与以往的DBM方法不同，该模型采用了自底向上的方法。采用Enskog碰撞模型描述了分子大小和排斥势的影响，通过平均场近似方法得到了吸引势。直接引入了导致非理想状态方程和表面张力的分子间相互作用作为外力项。对库埃特流、两相共存曲线、拉普拉斯定律、相分离、液滴碰撞等典型的基准问题进行了数值模拟，验证了模型的正确性。特别地，对于两种液滴碰撞，比较研究了由$(f - f ^{eq})$的二阶和三阶非守恒动力学矩定义的两种非平衡效应$\bar{D}_2^*$和$\bar{D}_3^*$的强度，其中$f$（$f^{eq}$）为平衡分布函数.有趣的是发现在碰撞过程中，$\bar{D}_2^*$总是明显大于$\bar{D}_3^*$，$\bar{D}_2^*$可以用来识别碰撞过程的不同阶段，区分不同类型的碰撞。对于非平衡效应较强、粘性应力的线性本构关系不再成立的情况，该建模方法可直接推广到高阶模型。
A simplified finite volume lattice Boltzmann method for simulations of fluid flows from laminar to turbulent regime, Part I: Numerical framework and its application to laminar flow simulation
