表征体元尺度渗流的离散统一动理学格式

结合表征体元尺度的通用渗流模型,提出离散统一动理学格式（DUGKS）渗流方法,分别用均匀网格和非均匀网格计算二维Poiseuille、Couette、方腔流等经典渗流问题,检验DUGKS渗流方法的有效性和非均匀网格应用的优势,将DUGKS渗流方法应用到裂缝系统中.     

热辐射输运问题的隐式蒙特卡罗方法求解

热辐射与物质相互作用及辐射光子在物质中的传输是惯性约束聚变研究中的重要课题. 介绍了基于隐式蒙特卡罗方法的辐射输运方程,在该方程的积分-微分形式基础上,推导了利于蒙特卡罗方法模拟的等价的积分输运方程;基于积分方程设计数值模拟流程,编写三维蒙特卡罗数值模拟程序;针对热辐射输运典型问题及benchmark问题开展了数值实验,计算结果验证了方法的适应性及程序的正确性. 关键词： 热辐射 惯性约束聚变 输运方程 隐式蒙特卡罗     

离散统一气体动理学格式的浸入边界方法

实现了离散统一气体动理学格式(DUGKS)与浸入边界(IB)方法的结合(IB-DUGKS)。通过Strang-splitting方法来引入外力,提高计算的稳定性。每一时间步先计算得到不考虑边界时的流场预估速度,通过多重直接力的方法计算受力,并对预估速度进行修正,使之满足无滑移边界条件。该方法结合了DUGKS与IB两者的优点。并且对于Taylor-Green涡、圆柱绕流及静止流体中的圆柱振荡问题进行模拟,模拟的结果与文献结果十分吻合。     

耦合辐射的三维热化学非平衡流数值模拟

发展耦合辐射的三维热化学非平衡流场计算方法,可用于非结构网格.采用Jameson有限体积法求解耦合辐射源项的三维N-S方程.辐射源项通过求解辐射输运方程(Radiative Transport Equation RTE)获得.在空间方向上离散后,采用有限体积法求解辐射输运方程.化学模型包含11个组元,20个化学反应.采用该数值方法计算MUSES-C模型在速度为11.6 km·s^-1时的绕流流场及前驻点处的辐射热流密度.并通过对比,分析热辐射对流场的影响.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

LARED集成程序辐射输运模拟的性能优化

分析定位高置信度辐射传输数值模拟效率瓶颈,针对物理模型和数值离散格式的特点,优化求解算法和程序设计,改进激光聚变二维总体LARED集成程序,提高输运建模模拟黑腔靶实验模型的计算效率：在相同的并行计算条件下,辐射输运方程离散求解计算效率提高2倍以上,全过程整体模拟计算时间减半.     

再入飞行器流场热辐射输运解算方法库研究

基于若干热辐射输运求解方法的一维辐射平衡和温度间断算例结果的对比分析,提出了一个由离散坐标法、P_1近似和光学厚度极限近似构建的热辐射输运解算方法库,该方法库可与再入飞行器热化学非平衡流场控制方程实现有效耦合模拟。利用该方法库模拟了60 km高空、马赫数35的球头算例,计算表明热辐射对高温流场具有显著的"冷却"作用;辐射传热与对流传热水平相当,流场非耦合热辐射计算的辐射热流将高出耦合计算值27%,此类飞行条件下的数值模拟研究应当考虑热辐射耦合效应。     

间断有限元法求解一维矢量辐射传输

采用间断有限元法(Discontinuous finite element method,DFEM)求解一维散射性介质内矢量辐射传输问题。推导了散射性介质内矢量辐射传输方程的间断有限元离散格式,空间离散采用间断有限元离散将求解域划分为相互独立的单元,角度离散在传统的均匀分段光滑近似(Piecewise Constant Approximation,PCA)角度离散基础上进行局部加密以得到关键方向上的数值解。采用两个稳态矢量辐射传输算例对间断有限元法求解矢量辐射传输方程的正确性和计算效率进行了验证,在此基础上拓展间断有限元法应用于求解散射性介质内瞬态矢量辐射传输方程,将随着时间推移过程中的瞬态辐射信息和最终的稳态结果相比较验证了本文方法的正确性。     

高温热辐射输运模拟的蒙特卡罗全局降方差方法

针对隐式蒙特卡罗方法模拟高温热辐射输运问题时存在的“辐射强度计算误差时间空间分布严重不均匀”现象,通过理论分析和数值模拟手段,找到决定误差大小的主要因素为“网格内的辐射径迹长度记录数”.据此提出“隐式蒙特卡罗全局降方差方法”并推导相应的计算公式.该方法主要包含如下3个关键技术:1)针对辐射输运蒙特卡罗模拟的自适应动态分配源粒子方法; 2)与自适应动态分配源粒子相匹配的动态权窗设计技术及粒子权无偏估计算法; 3)辐射强度的解析估计降方差方法.针对这3个关键技术,设计蒙特卡罗数值模拟方案,编写相应的数值模拟程序模块.典型辐射输运问题模拟结果显示:隐式蒙特卡罗全局降方差方法能够使网格辐射强度计算误差在整个时空范围内分布相对比较均匀,最大误差可控,计算效率提升10倍左右.新方法在激光惯性约束聚变的黑腔辐射输运模拟应用中取得了显著效果.     

一种求解三维热辐射输运方程的整体预处理迭代方法及并行计算

为三维灰体热辐射输运方程的隐式离散纵标方法发展一个整体预处理迭代方法并研制并行程序。该方法采用组装线性代数方程组策略,同时求出所有离散方向上的辐射强度。借助预处理的Krylov子空间迭代法,避免复杂网格上扫描算法可能遇到的死锁问题,能够提高健壮性和计算效率。空间离散上采用一阶迎风有限体积格式。数值实验测试变形六面体网格上的收敛率、评估预处理迭代方法的性能并计算辐射和物质的耦合问题,给出三维弯管和黑腔问题的模拟结果,验证程序的正确性和方法的适应性。     

A unified gas-kinetic scheme for continuum and rarefied flows

With discretized particle velocity space, a multiscale unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the BGK model. The current scheme couples closely the update of macroscopic conservative variables with the update of microscopic gas distribution function within a time step. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate Navier–Stokes (NS) solutions in the continuum flow regime with a time step being much larger than the particle collision time. At the same time, the rarefied flow solution, even in the free molecule limit, can be captured accurately. The unified scheme is an extension of the gas-kinetic BGK-NS scheme from the continuum flow to the rarefied regime with the discretization of particle velocity space. The success of the method is due to the un-splitting treatment of the particle transport and collision in the evaluation of local solution of the gas distribution function. For these methods which use operator splitting technique to solve the transport and collision separately, it is usually required that the time step is less than the particle collision time. This constraint basically makes these methods useless in the continuum flow regime, especially in the high Reynolds number flow simulations. Theoretically, once the physical process of particle transport and collision is modeled statistically by the kinetic Boltzmann equation, the transport and collision become continuous operators in space and time, and their numerical discretization should be done consistently. Due to its multiscale nature of the unified scheme, in the update of macroscopic flow variables, the corresponding heat flux can be modified according to any realistic Prandtl number. Subsequently, this modification effects the equilibrium state in the next time level and the update of microscopic distribution function. Therefore, instead of modifying the collision term of the BGK model, such as ES-BGK and BGK–Shakhov, the unified scheme can achieve the same goal on the numerical level directly. Many numerical tests will be used to validate the unified method.     

Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

In the previous multiscale finite-volume (MSFV) method, an efficient and accurate multiscale approach was proposed to solve the elliptic flow equation. The reconstructed fine-scale velocity field was then used to solve the nonlinear hyperbolic transport equation for the fine-scale saturations using an overlapping Schwarz scheme. A coarse-scale system for the transport equations was not derived because of the hyperbolic character of the governing equations and intricate nonlinear interactions between the saturation field and the underlying heterogeneous permeability distribution. In this paper, we describe a sequential implicit multiscale finite-volume framework for coupled flow and transport with general prolongation and restriction operations for both pressure and saturation, in which three adaptive prolongation operators for the saturation are used. In regions with rapid pressure and saturation changes, the original approach, with full reconstruction of the velocity field and overlapping Schwarz, is used to compute the saturations. In regions where the temporal changes in velocity or saturation can be represented by asymptotic linear approximations, two additional approximate prolongation operators are proposed. The efficiency and accuracy are evaluated for two-phase incompressible flow in two- and three-dimensional domains. The new adaptive algorithm is tested using various models with homogeneous and heterogeneous permeabilities. It is demonstrated that the multiscale results with the adaptive transport calculation are in excellent agreement with the fine-scale solutions. Furthermore, the adaptive multiscale scheme of flow and transport is much more computationally efficient compared with the previous MSFV method and conventional fine-scale reservoir simulation methods.     

Heat Flux for a Relativistic Dilute Bidimensional Gas

Relativistic kinetic theory predicts substantial modifications to the dissipation mechanisms of a dilute gas. For the heat flux, these include (in the absence of external forces) a correction to the thermal conductivity and the appearance of a new, purely relativistic, term proportional to the density gradient. In this work we obtain such constitutive equation for the particular case of a bidimensional gas. The calculation is based on the Chapman–Enskog solution to the relativistic Boltzmann equation and yields analytical expressions for the corresponding transport coefficients, which are evaluated for the particular case of hard disks. These results will be useful for numerical simulations and may be applied to bidimensional non-dense materials.     

Computer simulation and analysis of technical characteristics of thermomolecular micropumps

Thermomolecular micropumps operating without moving mechanical parts, differing in shape, but based on the same physical effect (thermal slip of a gas along nonuniformly heated walls) are investigated. The applicability of computer simulation methods and software in analysis of physical properties of various micropumps is demonstrated. As operation criteria, the pressure ratio produced by a pump in the steady-state operation regime and the geometry of the pump structure required for using the device in MEMS systems are employed. Functional capabilities of the pumps are studied numerically by computer simulation of the Boltzmann kinetic equation.     

A theory of Doppler and binary collision broadening by foreign gases—I: Formal theory

The quantum theory of combined Doppler and foreign gas pressure broadening at the binary collision level is developed from the point of view of statistical mechanics. A kinetic equation is first derived which is linearized in the radiation field. For line-broadening purposes, this equation is reduced to a steady-state equation for collisions localized in position space. The equation takes into account the effects of photon recoil momentum, binary collision correlations, collisions of finite duration and line-coupling.     

Transport Equations of Plasma in a Curvilinear Magnetic Field

The problem of transport equations of a collisional plasma in a curvilinear magnetic field is studied. Two main approaches to this problem are presented: that based on using the Boltzmann kinetic equation and the drift kinetic equation approach. In the frame of the first approach a multimoment transport equation set is found which is more general than the transport equation sets of Braginskii and Grad. The tensor equations of this set are described in an arbitrary curvilinear coordinate system. This allow to use these equations in problems of a plasma confined in toroidal magnetic configurations. Simplification of the multimoment transport equation set in the case of high magnetic field is performed. In the frame of the drift kinetic equation approach, a generalization of the drift transport equations derived earlier by the authors (Zh. Eksp. Teor. Fiz. 83 (1982) 139) is given.     

Nonlinear effects in damping of a standing wave in a gas

The problem of constructing of a uniform asymptotic approximation to the solution of the Boltzmann equation is solved for an attenuating small-amplitude standing wave in a stationary homogeneous gas in the limiting case of small Knudsen numbers ɛ. Using the multiscale technique, a regular approximation valid for time intervals up to ɛ⁻¹ is obtained. It is shown that nonlinearity of the kinetic equation leads to violation of monochromaticity of the initial perturbation and changes the damping mode.