缝洞型介质流动模拟的多尺度分解法

缝洞型介质通常具有非均质性强、结构多尺度的特征.传统数值方法在解决此类多尺度流动问题时,难以兼顾计算精度与计算效率,无法实际应用.对此,本文提出了多孔介质流体流动的多尺度分解法,并应用于缝洞介质流动模拟,能够大幅减小计算的复杂度,同时,可以通过控制均化程度控制计算精度.该方法将求解空间分为若干个子空间的正交直和,从而获得一个近线性的计算复杂度;以分层计算的方式实现了快速计算,另外这种方法是一种无网格方法,具有较好的地层适应性.同时,采用离散缝洞模型简化缝洞结构,进一步提高了计算效率.详细阐述了基于多尺度分解法的多孔介质流体流动数值计算格式的建立,重点介绍了如何在不同的层次上计算基函数.数值结果表明,本文提出的计算方法不仅能够准确捕捉多孔介质中的精细流动特征,而且具有很高的计算效率,是一种有效的流动模拟方法.     

基于离散裂缝模型的裂缝性油藏注水开发数值模拟

针对目前裂缝性油藏数值模拟方法存在的问题,基于单裂缝等效的概念,建立离散裂缝模型.对宏观大裂缝进行显式降维处理,在保证高计算效率的同时能够真实地反映裂缝对整个油藏流体流动的影响.详细阐述模型的基本原理,基于Galerkin加权残量法推导有限元数值计算格式,实现二维问题的数值模拟,通过算例验证模型和算法的正确性.以此为基础,分析裂缝对注水开发效果的影响.计算结果表明,对于裂缝发育程度不高尤其是当油藏中存在数条控制着流体流动方向的大裂缝时,离散裂缝模型具有很好的适用性.     

激光辐照受拉铝板破坏行为的时空多尺度数值模拟

推导耦合过渡区内参变量信息交换的元/网格动量传递多尺度算法,建立离散元与有限元耦合时空多尺度计算模型,并应用于激光辐照下受拉铝板破坏行为的数值模拟中.通过对比有限元计算模型、空间多尺度计算模型与时空多尺度计算模型在激光辐照下受拉铝板破坏算例的模拟结果,验证离散元与有限元耦合时空多尺度计算模型的准确性和数值计算高效率优势.使用该多尺度计算模型从宏观和细观尺度对铝板破坏行为进行数值模拟,模拟结果与实验结果基本一致.     

使用混合网格计算非达西渗流

针对垂直裂缝井的特殊流动模式,从非达西定律出发,建立二维平面的非达西渗流方程.通过建立一组无量纲量,最终得到无量纲的渗流方程及其定解条件.假定外边界为圆形,用PEBI网格及混合网格对求解区域进行网格划分,用有限差分法对无量纲的方程进行离散,最终得到垂直裂缝井的井底压力数值解.根据此数值解并考虑井筒存储和表皮因子的影响,得到真实垂直裂缝井的井底压力.对计算结果的分析表明,使用混合网格求解非达西渗流井底压力相当准确,该方法也适用于水平井等更复杂井型及复杂边界的问题求解.     

神经网络对于翼型绕流流场的重构

本文试图通过神经网络重构二维低雷诺数翼型绕流非定常流场。首先通过局部径向基函数(LRBF)求解器求解不可压缩流动控制方程得到计算域内流场信息,然后随机选取一些时空域内的数据点(包含位置信息和速度信息)作为训练数据代入神经网络进行训练。先学习训练得到流动的雷诺数后进行流场的重构,并与LRBF求解器得到的数值结果进行对比。流动计算中雷诺数设置为200,攻角为20°,计算域离散采用局部节点加密技术以减少计算量。     

粘性不可压流的变分多尺度数值模拟

在变分多尺度的理论框架内,将待求解的各个物理量分解到"粗"、"细"两种尺度上.在"细"尺度上采用"泡"函数作为近似函数,通过Petrov-Galerkin方法得到"细"尺度上的近似解;然后引入求解"粗"尺度方程所需的稳定项及与其相适应的稳定化因子;最后运用有限元方法求解"粗"、"细"两种尺度耦合的整体变分多尺度方程,得到有限元近似解.数值算例表明,该处理方法成功地消除了数值求解粘性不可压Navier-Stokes方程过程中,由对流占优和速度-压力失耦引起的数值伪振荡;所引入的稳定化因子适用于结构网格及非结构网格上的数值计算.     

大雷诺数Navier-Stokes方程的两水平亚格子模型稳定化方法

基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性.     

多孔介质模型在管壳式换热器数值模拟中的应用

本文详细讨论了多孔介质模型在管壳式换热器数值模拟中的应用,开发了一套能自动生成多孔介质特性参数的通用程序。该程序主要基于三维交错网格及SIMPLE算法,然后运用该模型,采用改进的κ-ε模型和壁面函数法,对换热器壳侧的湍流流动进行了数值模拟。计算结果与换热器冷态实验结果符合良好,表明该模型和计算方法是切实可行的。     

非定常Navier-Stokes方程基于两重网格离散的有限元并行算法

基于两重网格离散和区域分解技巧，提出三种求解非定常Navier-Stokes方程的有限元并行算法.算法的基本思想是在每一时间迭代步，在粗网格上采用Oseen迭代法求解非线性问题，在细网格上分别并行求解Oseen、Newton、Stokes线性问题以校正粗网格解.对于空间变量采用有限元离散，时间变量采用向后Euler格式离散.数值实验验证了算法的有效性.     

一种求解流体力学方程组的自适应显式时间积分算法及其应用

针对交替方向显式离散格式,提出一个基于结构网格局部加密技术(SAMR)的求解流体力学方程组的自适应时间积分算法;基于该算法,在JASMIN框架上研制多介质流体力学并行自适应数值模拟程序;在512个处理器上模拟惯性约束聚变中的二维内爆模型.数值模拟结果和并行性能分析显示了算法的正确性和并行实现的高效率.     

A hierarchical fracture model for the iterative multiscale finite volume method

An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.     

Local–global multiscale model reduction for flows in high-contrast heterogeneous media

In this paper, we study model reduction for multiscale problems in heterogeneous high-contrast media. Our objective is to combine local model reduction techniques that are based on recently introduced spectral multiscale finite element methods (see [19]) with global model reduction methods such as balanced truncation approaches implemented on a coarse grid. Local multiscale methods considered in this paper use special eigenvalue problems in a local domain to systematically identify important features of the solution. In particular, our local approaches are capable of homogenizing localized features and representing them with one basis function per coarse node that are used in constructing a weight function for the local eigenvalue problem. Global model reduction based on balanced truncation methods is used to identify important global coarse-scale modes. This provides a substantial CPU savings as Lyapunov equations are solved for the coarse system. Typical local multiscale methods are designed to find an approximation of the solution for any given coarse-level inputs. In many practical applications, a goal is to find a reduced basis when the input space belongs to a smaller dimensional subspace of coarse-level inputs. The proposed approaches provide efficient model reduction tools in this direction. Our numerical results show that, only with a careful choice of the number of degrees of freedom for local multiscale spaces and global modes, one can achieve a balanced and optimal result.     

二维非均匀多孔介质中不可压两相驱替的有限分析算法

为提高油藏数值模拟算法的计算效率,在求解单向稳态渗流的有限分析算法基础上,构建二维非均匀多孔介质中不可压两相渗流的有限分析算法.算法中,网格界面上的平均渗透率不是简单地取为相邻网格渗透率的调和平均值,而是通过奇点邻域解析解积分求得.相比于传统的数值算法,有限分析算法随着网格的加密,能够很快地收敛(仅需将原始网格细分至2×2或3×3),并且其计算精度和收敛性不依赖于介质的非均匀强度,从而计算效率得到提高.     

三维非均匀不稳定渗流方程的自适应网格粗化算法

将渗透率自适应网格技术应用于三维非均匀不稳定渗流方程的网格粗化算法中,在渗透率或孔隙度变化异常区域自动采用精细网格,用直接解法求解渗透率或孔隙度变化异常区域的压强分布,在其它区域采用不均匀网格粗化的方法计算,即在流体流速大的区域采用精细网格.用该方法计算了三维非均匀不稳定渗流场的压降解,结果表明三维非均匀不稳定渗流方程的三维非均匀自适应网格粗化算法的解在渗透率或孔隙度异常区的压强分布规律与采用精细网格的解非常逼近,在其它区域压强分布规律与粗化算法的解非常逼近,计算速度比采用精细网格提高100多倍.     

随机多孔介质的蒙特卡罗重构与渗流特性模拟

根据多孔介质微观结构的分形尺度标度特征,采用蒙特卡罗方法分别重构随机多孔介质的微观颗粒和孔隙结构,并基于分形毛管束模型研究多尺度多孔介质的气体渗流特性,建立多孔介质微观结构和宏观渗流特性的定量关系。结果表明：分形蒙特卡罗重构的多孔介质微细结构接近真实介质结构,气体渗流特性的计算结果与格子玻尔兹曼模拟数据较为吻合; 多孔介质气体渗透率随着克努森数的增加而增大,孔隙分形维数对于气体渗流的微尺度效应具有显著影响,而迂曲度分形维数对于表观渗透率和固有渗透率的比值影响可以忽略。提出的分形蒙特卡罗方法具有收敛速度快且计算误差与维数无关的优点,有利于深入理解多尺度多孔介质的渗流机理。     

A stochastic multiscale framework for modeling flow through random heterogeneous porous media

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes.A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given.     

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.     

Numerical methods for multiscale transport equations and application to two-phase porous media flow

We discuss numerical methods for linear and nonlinear transport equations with multiscale velocity fields. These methods are themselves multiscaled in nature in the sense that they use macro and micro grids, multiscale test functions. We demonstrate the efficiency of these methods and apply them to two-phase flow in heterogeneous porous media.     

Variational multiscale turbulence modelling in a high order spectral element method

In the variational multiscale (VMS) approach to large eddy simulation (LES), the governing equations are projected onto an a priori scale partitioning of the solution space. This gives an alternative framework for designing and analyzing turbulence models. We describe the implementation of the VMS LES methodology in a high order spectral element method with a nodal basis, and discuss the properties of the proposed scale partitioning. The spectral element code is first validated by doing a direct numerical simulation of fully developed plane channel flow. The performance of the turbulence model is then assessed by several coarse grid simulations of channel flow at different Reynolds numbers.     

Multiscale finite element methods for high-contrast problems using local spectral basis functions

In this paper we study multiscale finite element methods (MsFEMs) using spectral multiscale basis functions that are designed for high-contrast problems. Multiscale basis functions are constructed using eigenvectors of a carefully selected local spectral problem. This local spectral problem strongly depends on the choice of initial partition of unity functions. The resulting space enriches the initial multiscale space using eigenvectors of local spectral problem. The eigenvectors corresponding to small, asymptotically vanishing, eigenvalues detect important features of the solutions that are not captured by initial multiscale basis functions. Multiscale basis functions are constructed such that they span these eigenfunctions that correspond to small, asymptotically vanishing, eigenvalues. We present a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/Λ₁)^1/2, where Λ₁ is proportional to the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space. Thus, we would like to reach to a larger eigenvalue with a smaller coarse space. This is accomplished with a careful choice of initial multiscale basis functions and the setup of the eigenvalue problems. Numerical results are presented to back-up our theoretical results and to show higher accuracy of MsFEMs with spectral multiscale basis functions. We also present a hierarchical construction of the eigenvectors that provides CPU savings.