Application of strand meshes to complex aerodynamic flow fields

We explore a new approach for viscous computational fluid dynamics calculations for external aerodynamics around geometrically complex bodies that incorporates nearly automatic mesh generation and efficient flow solution methods. A prismatic-like grid using “strands” is grown a short distance from the body surface to capture the viscous boundary layer, and adaptive Cartesian grids are used throughout the rest of the domain. The approach presents several advantages over established methods: nearly automatic grid generation from triangular or quadrilateral surface tessellations, very low memory overhead, automatic mesh adaptivity for time-dependent problems, and fast and efficient solvers from structured data in both the strand and Cartesian grids.The approach is evaluated for complex geometries and flow fields. We investigate the effects of strand length and strand vector smoothing to understand the effects on computed solutions. Results of three applications using the strand-adaptive Cartesian approach are given, including a NACA wing, isolated V-22 (TRAM) rotor in hover, and the DLR-F6 wing-body transport. The results from these cases show that the strand approach can successfully resolve near-body and off-body features as well as or better than established methods.     

Solving Navier–Stokes equation for flow past cylinders using single-block structured and overset grids

Many complex fluid motions are driven by physical processes of instability, transition and turbulence dependent upon nonlinear mechanisms. Here, we solve the flow past cylinder(s) using single-block structured and overset grids by computing Navier–Stokes equation in two-dimensions. The suitability of a compact scheme in discretizing convection and diffusion terms are investigated first by looking at relevant numerical properties. Also, for the overset grid method, one of the methods is identified that shows the best results in minimizing interpolation error at sub-domain boundaries for an analytical test function. We provide extensive comparisons with experimental and other computational results for flow past a single cylinder, utilizing both single-block structured and Chimera or overset grids. Apart from showing instability of this flow calculated by these methods, we also compare the computed vorticity and velocity data using these two grids by employing the proper orthogonal decomposition (POD). We have analyzed and developed an overset grid method with compact scheme that does not need any filtering to control error. This has been ascertained by performing POD analysis. To show that the developed method is capable of handling complex geometries, we have computed flow past two cylinders in side-by-side arrangement. Results obtained capture the known flow characteristics for this arrangement well using relatively fewer number of grid points.     

A fast adaptive quadtree scheme for a two-layer shallow water model

This paper presents a dynamically adaptive quadtree grid generation system for the solution of a two-dimensional two-layer shallow water model. Roe-type two-layer shallow water solvers require numerical approximation of the system eigenvalues as well as numerical balancing, which increase computational cost considerably when a regular grid is used. In order to improve computational efficiency, we consider a dynamically adaptive quadtree grid generation system capable of increasing local resolution where high gradients occur in the physical flow variables. Test results show that satisfactory convergence can be obtained using the present scheme with the adaptive grid generator at a fraction of the cost incurred by a regular grid.     

复杂外形静动态混合网格生成技术研究新进展

网格生成技术是CFD复杂工程应用的重要环节, 网格质量的好坏直接影响计算结果的精准度, 因此其已成为CFD的重要研究领域.在张涵信院士的指导下, 作者自20世纪90年代初开始开展非结构网格、混合网格技术和相应的计算方法研究, 并逐步发展至动态混合网格技术及非定常计算方法.在张涵信院士80华诞之际, 对近年来作者及团队在网格生成技术及应用方面所取得的进展进行了简要的综述, 分别介绍了静动态混合网格生成、定常/非定常计算方法、网格技术的应用等方面的进展情况.最后, 就网格生成技术目前还存在的问题, 展望了未来的发展方向.作者谨以此文表达对张涵信院士25年来的培养、关怀和帮助的崇高敬意.      

An adaptive algorithm for simulation of stochastic reaction–diffusion processes

We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction–diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie’s stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.     

高雷诺数双螺旋涡尾迹演化特性分析

螺旋状尾迹涡是直升机悬停旋翼流场的主导特征之一,其时空演化特性对旋翼气动性能具有重要影响.为了揭示悬停状态下旋翼尾迹涡的演化特征,对两桨叶刚性旋翼在高雷诺数悬停状态下的双螺旋状尾迹涡开展数值研究,采用基于流场特征的网格自适应技术,结合低耗散迎风/中心混合格式以及延迟脱体涡模拟方法对Caradonna-Tung旋翼在桨尖马赫数为0.439、桨尖雷诺数为1.92×10~6的悬停流场进行了高分辨率计算.基于欧拉和拉格朗日两种描述方法对计算结果进行了分析,揭示了双螺旋尾涡系统的演化特性:后缘尾涡面在桨尖附近的反向卷起及其与下游桨尖涡的相互作用是影响涡系稳定性以及涡-涡相互作用的重要因素;涡龄小于720°时,在固连于桨叶上的旋转坐标系中观察,涡系具有时空稳定性,涡管中心处轴向涡量随涡龄按照幂函数规律衰减.在固连于漩涡中心的局部极坐标系中,周向速度分布以及涡核半径随涡龄的变化与理论涡模型相符合,环量随涡龄的变化显示了漩涡的生长、平衡及耗散等演化阶段;模态分析结果表明,除点涡模态外,来流与点涡的复合模态在漩涡演化过程中对流动特征的转变有重要影响;涡系轴截面速度场的拉格朗日拟序结构直观地显示了漩涡场的时空演化过程,揭示了漩涡配对和共旋穿越等流动特征,同时也展示了后缘尾涡面卷起现象在漩涡演化过程中的作用.     

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.     

The computation of axisymmetric, supersonic nozzle arc usingadaptive grids

The computational difficulties associated with an arc burning in an axisymmetric supersonic nozzle are mainly caused by the region (known as the boundary) surrounding the are core within which temperature changes rapidly. When the arcing current decreases, this boundary collapses rapidly towards the axis. An adaptive grid scheme based on the temperature gradient is used to solve the dynamic are conservation equations in the computational domain. A direct grid adaptive scheme relates the solution in the computational domain to that in the physical domain without interpolation. Numerical results are compared with the experimental results as well as other numerical solutions obtained respectively by using a uniformly distributed, fixed grid system in the physical domain and by the solution adjusted method. A good agreement is achieved     

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang–Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.     

一种非定常N-S方程并行求解设计

为了解决计算流体力学(CFD)中非定常计算与越来越大的计算量,并行计算已成为一种现实有效的选择.论文首先研究了一种并行区域分解策略,该策略简单而高效,但需要算法配合.为此,采用了一种与并行完全兼容的隐式方法DP-LUR方法.通过双时间步长法,将DP-LUR方法延伸应用到非定常计算中而不改变其原有的性质.最后分析了并行编程中的主要难点,提出解决方法,即采用中间数据分离节点下标与处理,并给出了并行程序的总体结构.     

An adaptive multi-grid chemistry (AMC) model for efficient simulation of HCCI and DI engine combustion

There is a need to reduce the computational expense of practical multidimensional combustion simulations. Simulation of Homogeneous Charge Compression Ignition (HCCI) engine processes requires consideration of detailed chemistry in order to capture the ignition and combustion characteristics. Even with relatively coarse numerical meshes and reduced chemistry mechanisms, calculation times are still unacceptably long. For the simulation of Direct Injection (DI) engines, fine meshes are needed to achieve the resolution required by the spray and mixing models, and they are computationally expensive even with reduced chemistry. In addition, the increasing application of CFD for engine design optimization is pushing the demand to reduce computational time. In current design optimizations, depending on the size of the parametric space, hundreds of individual simulations are needed.

This work presents an efficient Adaptive Multi-grid Chemistry (AMC) model that can be used in engine CFD codes for simulations of HCCI and DI engines with detailed chemistry. It was found that the number of cells computed with the chemistry solver can be reduced by two orders of magnitude for HCCI engines. The results predicted by the present KIVA AMC code are also consistent with those calculated by the original code using every cell.

In the method, progressively coarser grids are used for cells with similar gas properties in the chemistry calculation (up to four neighbour levels) or in the global method, cells are grouped without regard for their locations in the cylinder. Averaged and gradient-preserving remapping techniques used in multi-zone engine simulations were also explored. A parametric study was conducted for determining the model variables, such as the degree of local homogeneity for the multi-grid solvers.

The simulation results were compared with experimental data obtained from a Honda engine operated with n-heptane under HCCI conditions for which directly measured in-cylinder temperature and H₂O mole fraction data are available. In addition, simulation results were found to agree well with experimental data from a DI diesel engine operated under PCCI conditions with ultra-high EGR rates. It was found that computer time was reduced by a factor of ten for HCCI cases and two to three for DI cases without losing prediction accuracy.     

A lagged implicit segregated data reconstruction procedure to treat open boundaries

The problem of treating open boundaries is still a challenging one. Applying fully developed condition is constrained to long enough domains. Without having enough physical evidence about what happens on boundaries, the domain extent could not be shortened and computational costs could not be reduced. From the advent of free (open) boundary conditions, they were confined to mixed finite element procedures. Recent works have extended their application to coupled finite volume solvers based on the shape function data reconstruction. A wider class of flow solvers available, however, rely on the segregated procedure where the velocity components and pressure are solved in succession. Moreover, many finite volume algorithms do not use the shape function reconstruction. In this work, by proposing a lagged implicit procedure, we have extended the application of the open boundary condition to these wider classes of flow solvers. The proposed extension is a combination of lagged implicit data reconstruction and overall mass conservation enforcement, which is easily applicable to any segregated and coupled flow solver. To validate the compatibility of this extension, benchmark problem of backward facing step is solved on successively truncated domains, where open boundary may pass through recirculation zones. Results show that the proposed extension works fine. For that problem, it reduced the computational domain length (and hence memory) by a factor of 4.6 and the required computational time by a factor of 21. Flow passing a cylinder is also solved which proves that the method could be applied to external flow problems as well.     

The surface roughness effect on the performance of supersonic ejectors

The paper presents the numerical simulation results of the surface roughness influence on gas-dynamic processes inside flow parts of a supersonic ejector. These simulations are performed using two commercial CFD solvers (Star- CCM+ and Fluent). The results are compared to each other and verified by a full-scale experiment in terms of global flow parameters (the entrainment ratio: the ratio between secondary to primary mass flow rate - ER hereafter) and local flow parameters distribution (the static pressure distribution along the mixing chamber and diffuser walls). A detailed comparative study of the employed methods and approaches in both CFD packages is carried out in order to estimate the roughness effect on the logarithmic law velocity distribution inside the boundary layer. Influence of the surface roughness is compared with the influence of the backpressure (static pressure at the ejector outlet). It has been found out that increasing either the ejector backpressure or the surface roughness height, the shock position displaces upstream. Moreover, the numerical simulation results of an ejector with rough walls in the both CFD solvers are well quantitatively agreed with each other in terms of the mean ER and well qualitatively agree in terms of the local flow parameters distribution. It is found out that in the case of exceeding the “critical roughness height” for the given boundary conditions and ejector’s geometry, the ejector switches to the “off-design” mode and its performance decreases considerably.     

An adaptive MHD method for global space weather simulations

A 3D parallel adaptive mesh refinement (AMR) scheme is described for solving the partial-differential equations governing ideal magnetohydrodynamic (MHD) flows. This new algorithm adopts a cell-centered upwind finite-volume discretization procedure and uses limited solution reconstruction, approximate Riemann solvers, and explicit multi-stage time stepping to solve the MHD equations in divergence form, providing a combination of high solution accuracy and computational robustness across a large range in the plasma β (β is the ratio of thermal and magnetic pressures). The data structure naturally lends itself to domain decomposition, thereby enabling efficient and scalable implementations on massively parallel supercomputers. Numerical results for MHD simulations of magnetospheric plasma flows are described to demonstrate the validity and capabilities of the approach for space weather applications     

A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen–Loève expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.     

并行重叠/变形混合网格生成技术及其应用

为了适用于柔性变形、相对运动等复杂动边界问题,建立了并行环境下重叠和变形相结合的动态混合网格生成技术.通过计算区域分解以及分布式并行实现了重叠和变形技术的结合,其中重叠网格采用了并行化的隐式装配方法,并发展了两种并行化查询策略.变形网格则采用了并行化的径向基函数（RBF）插值方法.并行化动态网格生成方法大幅提高了动态网格生成效率,有利于处理大规模的动边界问题.在此基础上,发展了基于变形/重叠动态混合网格的流动/运动/控制一体化数值模拟方法,进一步改进了耦合模拟软件平台——HyperFLOW.典型应用算例证明了该动态混合网格技术及一体化算法的实用性.      

多级轴流压气机三维数值优化设计

开发了利用非均匀有理B样条对叶轮机械三维叶片进行参数化重构的叶片造型模块和提供多种优化方法的优化模块;集成上述模块以及自主开发的网格生成软件和流场求解软件,建立了压气机气动数值优化平台.在该平台上对某5级轴流压气机末级静子进行了气动数值优化设计,取得了良好的优化效果,压气机性能得到有效提高.     

Nonuniform time-step Runge–Kutta discontinuous Galerkin method for Computational Aeroacoustics

With many superior features, Runge–Kutta discontinuous Galerkin method (RKDG), which adopts Discontinuous Galerkin method (DG) for space discretization and Runge–Kutta method (RK) for time integration, has been an attractive alternative to the finite difference based high-order Computational Aeroacoustics (CAA) approaches. However, when it comes to complex physical problems, especially the ones involving irregular geometries, the time step size of an explicit RK scheme is limited by the smallest grid size in the computational domain, demanding a high computational cost for obtaining time accurate numerical solutions in CAA. For computational efficiency, high-order RK method with nonuniform time step sizes on nonuniform meshes is developed in this paper. In order to ensure correct communication of solutions on the interfaces of grids with different time step sizes, the values at intermediate-stages of the Runge–Kutta time integration on the elements neighboring such interfaces are coupled with minimal dissipation and dispersion errors. Based upon the general form of an explicit p-stage RK scheme, a linear coupling procedure is proposed, with details on the coefficient matrices and execution steps at common time-levels and intermediate time-levels. Applications of the coupling procedures to Runge–Kutta schemes frequently used in simulation of fluid flow and acoustics are given, including the third-order TVD scheme, and low-storage low dissipation and low dispersion (LDDRK) schemes. In addition, an analysis on the stability of coupling procedures on a nonuniform grid is carried out. For validation, numerical experiments on one-dimensional and two-dimensional problems are presented to illustrate the stability and accuracy of proposed nonuniform time-step RKDG scheme, as well as the computational benefits it brings. Application to a one-dimensional nonlinear problem is also investigated.     

5×5棒束CFD模拟计算域和网格标准

采用不可压N-S方程、标准k-ε湍流模型、SIMPLE算法,对某压水堆的两跨距5×5燃料组件的水循环区域流动进行数值分析.对比流道横截面上的压降、速度及其横向分量的相对误差,得到计算域的进出口段长度、网格形式、网格尺寸的选取标准.结果显示：计算域的进口段、出口段长度不宜过短或过长,分别为2.0倍、2.3~2.8倍格架中心距长度;格架区宜采用非结构蜂窝网格,光棒区宜采用结构网格;格架区网格尺寸可取0.3 mm,最大不宜超过0.35 mm,而结构网格横向尺寸可取0.3 mm~0.5 mm,纵向稀疏比应小于1.5为宜.满足上述标准,数值分析能保证较高的可信度,同时保持可接受的计算量.     

A multi-resolution,non-parametric,Bayesian framework for identification of spatially-varying model parameters

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in PDE-based models and correspond to quantities such as density or pressure fields, elasto-plastic moduli and internal variables in solid mechanics, conductivity fields in heat diffusion problems, permeability fields in fluid flow through porous media etc. The proposed model has all the advantages of traditional Bayesian formulations such as the ability to produce measures of confidence for the inferences made and providing not only predictive estimates but also quantitative measures of the predictive uncertainty. In contrast to existing approaches it utilizes a parsimonious, non-parametric formulation that favors sparse representations and whose complexity can be determined from the data. The proposed framework in non-intrusive and makes use of a sequence of forward solvers operating at various resolutions. As a result, inexpensive, coarse solvers are used to identify the most salient features of the unknown field(s) which are subsequently enriched by invoking solvers operating at finer resolutions. This leads to significant computational savings particularly in problems involving computationally demanding forward models but also improvements in accuracy. It is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling which is embarrassingly parallelizable and circumvents issues with slow mixing encountered in Markov Chain Monte Carlo schemes. The capabilities of the proposed methodology are illustrated in problems from nonlinear solid mechanics with special attention to cases where the data is contaminated with random noise and the scale of variability of the unknown field is smaller than the scale of the grid where observations are collected.