Generalized characteristic interface conditions for high-order multi-block computation

In practical fluid computation with structured grids around complex geometries, singular points with metric discontinuity can frequently be found. Generally, the grid singularities may cause numerical oscillations when some high-order finite difference scheme is applied. Recently, an excellent theory has been proposed which solves the above singular problem by block decomposition along the singular surface and by imposition of the characteristic interface conditions (CIC) on the block interface. However, the original theory has constraints on the mathematical treatment of the block interface, and therefore prevents numerical flexibility from a practical point of view. In this article, in order to extend the functions of the original CIC, we propose the generalized characteristic interface conditions (GCIC). Proper numerical test analysis is conducted to validate the performance of the GCIC, and as a practical application, multi-block computation is performed with the GCIC applied to complex geometry.     

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing the period boundary condition, the computation regions of flows are discretized by using the structured chimera grids composed of a fine rotor grid and a cylindrical background grid. In the background grid, the mesh cells located in the wake regions are refined after the solution reaches the approximate convergence. Considering the interpolation characteristic of the WENO scheme, three layers of the hole boundary and the interpolation boundary are searched. The performance of the schemes is investigated in a transonic flow and a subsonic flow around the hovering rotor. The results reveal that the present approach has great capabilities in capturing the vortex wake with high resolution, and the WENO scheme has much lower numerical dissipation in comparison with the MUSCL scheme.     

A technique of flux reconstruction at the interfaces of nonconforming grids for aeroacoustic simulations

A flux reconstruction technique is presented to perform aeroacoustic computations using implicit high-order spatial schemes on multiblock structured grids with nonconforming interfaces. The use of such grids, with mesh spacing discontinuities across the block interfaces, eases local mesh refinements, simplifies the mesh generation process, and thus facilitates the computation of turbulent flows. In this work, the spatial discretization consists of sixth-order finite-volume implicit schemes with low-dispersion and low-dissipation properties. The flux reconstruction is based on the combination of noncentered schemes with local interpolations to define ghost cells and compute flux values at the grid interfaces. The flow variables in the ghost cells are calculated from the flow field in the grid cells using a meshless interpolation with radial basis functions. In this study, the flux reconstruction is applied to both plane and curved nonconforming interfaces. The performance of the method is first evaluated by performing two-dimensional simulations of the propagation of an acoustic pulse and of the convection of a vortex on Cartesian and wavy grids. No significant spurious noise is produced at the grid interfaces. The applicability of the flux reconstruction to a three-dimensional computation is then demonstrated by simulating a jet at a Mach number of 0.9 and a diameter-based Reynolds number of 4×10⁵ on a Cartesian grid. The nonconforming grid interface located downstream of the jet potential core does not appreciably affect the flow development and the jet sound field, while reducing the number of mesh points by a factor of approximately two.     

Estimate of the truncation error of finite volume discretization of the Navier–Stokes equations on colocated grids

A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier–Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two‐dimensional flows, but extension to three‐dimensional cases should not pose problems. Copyright © 2005 John Wiley & Sons, Ltd.     

CFD多块网格生成新进展

网格生成是计算流体力学的重要组成部分,多块网格在CFD实践中获得了广泛的应用．结合对网格生成技术规范和网格生成系统的讨论,综述了多块网格近年来的新进展,重点评述了网格拓扑和网格拼接技术（包括所谓的连续拼接、非结构拼接和广义拼接）,完整飞机外形多块网格生成策略,自动分块技术以及相应的块合井技术,CAD和CFD之间的数据交换技术和基于NURBS的曲面网格生成技术,网格质量分析和控制技术,若干网格生成新方法,以及多块网格在航空气动力数值模拟中的应用．      

一种快速稳健的并行多块结构动网格方法

为解决传统网格处理方法不能满足复杂外形在大设计空间内进行优化时对网格质量的要求的问题,提出了一种并行多块动网格方法,该方法基于初始外形的多块结构网格,根据优化过程中个体外形与初始外形拓扑结构相近的特性,利用体样条插值方法来拟合多块结构网格各块顶点的位移,得到几何外形变化后的拓扑结构,再利用无限插值方法并行地移动初始外形多块结构网格的边、面和块内的网格点,进行光顺处理后得到变形后几何外形的空间网格;该方法在保证网格质量的同时,可以极大地提高网格生成效率,本文以某翼身组合体为例结果表明,该方法在大设计空间的复杂外形设计问题中具有很强的实用性。     

Computational properties of vertical grids for a nonhydrostatic anelastic model

Computational dispersion properties of all vertically staggered grids, which are presently available, are analysed in terms of frequency and group velocity components using the second-order centre difference scheme for a nonhydrostatic anelastic approximation system with a general method. The inertial-gravitational waves with a horizontal scale of a hundred-, ten- and one-kilometres are considered. The comparison analysis shows that the Charny-Phillips (CP) and Lorenz grids are suitable for waves at all abovementioned horizontal scales, while the Lorenz time staggered and Charny-Phillips time staggered grids are applicable only to waves with a horizontal scale less than 10 km. The unstaggered (N) grid is not suitable for simulating waves at any horizontal scale. In an idealised flow numerical test, the result on the CP grid has much less error than that on the N grid.     

Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries

This paper proposes an extension scheme for the application of the single phase multi-block lattice Boltzmann method (LBM) to the multiphase Gunstensen model, in which the grid is refined in a specific part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows, and it was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant drop in a parabolic flow.     

翼吊式双发民机机体/动力装置一体化数值分析

介绍了多块网格技术与流场分区求解方法在翼吊式双发民机机体／动力装置一体化研究中的应用。数值求解Ｅｕｌｅｒ方程模拟复杂组合体绕流。采用边界层方程／Ｅｕｌｅｒ方程耦合迭代技术进行翼面粘性修正。为保持Ｅｕｌｅｒ注解中计算网格固定,粘流／无粘流耦合迭采用表面源模型。该方法对某民用飞机模型跨音速绕流流场进行了数值模拟,机翼表面计算压力分布与实验吻合良好。     

Scientific post hoc and in situ visualisation of high-order polynomial solutions from massively parallel simulations

This paper presents two recent numerical tools developed respectively to perform traditional post-processing and more advanced in situ processing of high-order polynomial data generated by massively parallel finite element codes. For post-processing and visualisation of high-order solutions, we present a new ParaView plugin that integrates Gmsh used as an external library. This plugin therefore combines respectively ParaView's scalability in parallel and Gmsh's ability to apply h-refinement of the initial mesh followed by solution interpolation on the resulting visualisation grid, thus enabling parallel visualisation of any arbitrary high-order polynomial solutions in client–server mode. In a second stage, this capacity has been extended to an in situ interface based on the Catalyst library which enables in situ analysis and visualisation of high-order solutions. These new capacities are demonstrated with the visualisation of high-order solution of the unsteady flow generated by a discontinuous Galerkin method for an unsteady turbomachinery application.     

A geometry‐based level set method for curvilinear overset grids with application to ship hydrodynamics

In a previous work (Int. J. Numer. Meth. Fluids 2007; 55 :867–897), we presented a two‐phase level set method to simulate air/water turbulent flows using curvilinear body‐fitted grids for ship hydrodynamics problems. This two‐phase level set method explicitly enforces jump conditions across the interface, thus resulting in a fully coupled representation of the air/water flow. Though the method works well with multiblock curvilinear grids, severe robustness problems were found when attempting to use it with overset grids. The problem was tracked to small unphysical level set discontinuities across the overset grids with large differences in curvature. Though negligible for single‐phase approaches, the problem magnifies with large density differences between the phases, causing computation failures. In this paper, we present a geometry‐based level set method for curvilinear overset grids that overcomes these difficulties. The level set transport and reinitialization equations are not discretized along grid coordinates, but along the upwind streamline and level set gradient directions, respectively. The method is essentially an unstructured approach that is transparent to the differences between overset grids, but still the discretization is under the framework of a finite differences approach. As a result, significant improvements in robustness and to a less extent in accuracy are achieved for the level set function interpolation between overset grids, especially with big differences in grid curvature. Example tests are shown for the case of bow breaking waves around the surface combatant model David Taylor Model Basin (DTMB) 5415 and for the steady‐state ONR Tumblehome DTMB 5613 with superstructure. In the first case, the results are compared against experimental data available and in the second against results of a semi‐coupled method. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic propagation simulation in complex media with non-rectangular irregular-grid finite-difference

This paper presents a finite-difference (FD) method with spatially non-rectangular irregular grids to simulate the elastic wave propagation. Staggered irregular grid finite difference operators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations. This method is very simple and the cost of computing time is not much. Complicated geometries like curved thin layers, cased borehole and nonplanar interfaces may be treated with nonrectangular irregular grids in a more flexible way. Unlike the multi-grid scheme, this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration. Compared with the rectangular irregular grid FD, the spurious diffractions from “staircase” interfaces can easily be eliminated without using finer grids. Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme. The Higdon‘s absorbing boundary condition is adopted to eliminate boundary reflections. Numerical simulations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces. The computation costs are less than those using a regular grid and rectangular grid FD method.     

Recent Development on the Conservation Property of Chimera

An estimate on the conservation error due to the non-conservative data interpolation scheme for overset grids is given in this paper. It is shown that the conservation error is a first-order term if second-order conservative schemes are employed for the Chimera grids and if discontinuities are located away from overlapped grid interfaces. Therefore in the limit of global grid refinement, valid numerical solutions should be obtained with a data interpolation scheme. In one demonstration case the conservation error in the original Chimera scheme was shown to affect flow even without discontinuities on coarse to medium grids. The conservative Chimera scheme was shown to give significantly better solutions than the original Chimera scheme on these grids with other factors being the same.     

A numerical study on a Cartesian-based body-fitted adaptive grid method

ABSTRACT

A hybrid Cartesian-based body-fitted adaptive grid method for compressible Navier–Stokes equations is implemented and investigated. In this method, the body-fitted structured grids are generated around the geometries, and the left regions are filled with Cartesian grids. To transfer the data between the different grids, the donor cell searching technique is adopted. An unstructured data-based finite volume update procedure is used, and least squares method is suggested to retain the second order in the overlap region. The moving shock waves with different speeds and vortex passing through the interfaces of the hybrid Cartesian grid are used to explore the accuracy and conservation. A new technique is presented to deal with the non-physical stagnation of slowly moving shock wave around the interface of grid. Numerical examples are presented to demonstrate the results. The three-dimensional extension has also been shown by a benchmark problem.     

An efficient and accurate algebraic interface capturing method for unstructured grids in 2 and 3 dimensions: The THINC method with quadratic surface representation

We present in this paper an efficient and accurate volume of fluid (VOF) type scheme to compute moving interfaces on unstructured grids with arbitrary quadrilateral mesh elements in 2D and hexahedral elements in 3D. Being an extension of the multi‐dimensional tangent of hyperbola interface capturing (THINC) reconstruction proposed by the authors in Cartesian grid, an algebraic VOF scheme is devised for arbitrary quadrilateral and hexahedral elements. The interface is cell‐wisely approximated by a quadratic surface, which substantially improves the numerical accuracy. The same as the other THINC type schemes, the present method does not require the explicit geometric representation of the interface when computing numerical fluxes and thus is very computationally efficient and straightforward in implementation. The proposed scheme has been verified by benchmark tests, which reveal that this scheme is able to produce high‐quality numerical solutions of moving interfaces in unstructured grids and thus a practical method for interfacial multi‐phase flow simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

THE PROGRESS OF THE OVERLAPPING GRID TECHNIQUES

从网格装配和插值计算两个主要方面对现有的重叠网格方法进行了综述。首先,从挖洞方法和建立嵌入网格关系环节的寻点技术出发归纳和介绍了网格装配方法;其次,介绍了数值迭代过程中的插值计算方法,并特别讨论了插值守恒性以及插值计算精度等问题;另外,对重叠网格方法的并行计算和应用成果也作了介绍;最后,通过总结认为重叠网格方法在改进网格装配方法、改善插值和并行计算效率等方面仍需进一步研究。     

Mie-Grneisen状态方程可压缩多流体流动的PPM方法

采用流体体积分数的混合型多流体数值模型，将piecewise parabolic method (PPM)方法应用于可压缩多流体流动的数值模拟，拓展了以前提出的模型和数值方法，使它能够处理一般的Mie-Grneisen状态方程。采用双波近似和两层迭代算法求解一般状态方程的Riemann问题；并根据多流体接触界面无振荡原则设计高精度计算格式，对典型的纯界面平移问题可以从理论上证明本算法在接触间断附近压力和速度没有振荡，而且数值模拟结果表明界面数值耗散也被控制在2~3个网格之内。模拟了多种复杂的可压缩多流体流动，算例结果表明本文方法可以有效地处理接触间断、激波等物理问题，且具有耗散小精度高的特点。     

爆炸冲击波强间断问题的高阶伪弧长算法研究

为了提高对冲击波强间断处的分辨率,通过引入弧长参数,使网格自适应地朝着间断处移动,并结合高精度WENO数值格式,进而达到了对大梯度物理量的高分辨率捕捉。针对网格移动造成的非均匀和非正交现象,通过坐标变换,使得计算过程在均匀正交的计算空间中进行。通过和有限体积下的数值结果对比,结合数值误差分析,可以看到高阶伪弧长数值算法不仅保证了高精度而且对间断的捕捉更加明显,在间断附近解的整体光滑性较好,网格的自适应移动使得解的奇异性得到了削弱,因此可以削弱高阶格式容易引起数值振荡这个缺点。最后采用高阶伪弧长算法计算了化学反应流问题,结果表明高阶伪弧长算法有着较快的收敛率,对于解决爆炸与冲击强间断问题有着较为明显的优势。     

A fast nested multi‐grid viscous flow solver for adaptive Cartesian/Quad grids

A nested multi‐grid solution algorithm has been developed for an adaptive Cartesian/Quad grid viscous flow solver. Body‐fitted adaptive Quad (quadrilateral) grids are generated around solid bodies through ‘surface extrusion’. The Quad grids are then overlapped with an adaptive Cartesian grid. Quadtree data structures are employed to record both the Quad and Cartesian grids. The Cartesian grid is generated through recursive sub‐division of a single root, whereas the Quad grids start from multiple roots—a forest of Quadtrees, representing the coarsest possible Quad grids. Cell‐cutting is performed at the Cartesian/Quad grid interface to merge the Cartesian and Quad grids into a single unstructured grid with arbitrary cell topologies (i.e., arbitrary polygons). Because of the hierarchical nature of the data structure, many levels of coarse grids have already been built in. The coarsening of the unstructured grid is based on the Quadtree data structure through reverse tree traversal. Issues arising from grid coarsening are discussed and solutions are developed. The flow solver is based on a cell‐centered finite volume discretization, Roe's flux splitting, a least‐squares linear reconstruction, and a differentiable limiter developed by Venkatakrishnan in a modified form. A local time stepping scheme is used to handle very small cut cells produced in cell‐cutting. Several cycling strategies, such as the saw‐tooth, W‐ and V‐cycles, have been studies. The V‐cycle has been found to be the most efficient. In general, the multi‐grid solution algorithm has been shown to greatly speed up convergence to steady state—by one to two orders. Copyright © 2000 John Wiley & Sons, Ltd.     

基于非结构/混合网格的高阶精度格式研究进展

尽管以二阶精度格式为基础的计算流体力学(CFD) 方法和软件已经在航空航天飞行器设计中发挥了重要的作用, 但是由于二阶精度格式的耗散和色散较大, 对于湍流、分离等多尺度流动现象的模拟, 现有成熟的CFD 软件仍难以给出满意的结果, 为此CFD 工作者发展了众多的高阶精度计算格式. 如果以适应的计算网格来分类, 一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法. 由于非结构/混合网格具有良好的几何适应性, 基于非结构/混合网格的高阶精度格式近年来备受关注. 本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展, 重点介绍了空间离散方法, 主要包括k-Exact 和ENO/WENO 等有限体积方法, 间断伽辽金(DG) 有限元方法, 有限谱体积(SV) 和有限谱差分(SD) 方法, 以及近来发展的各种DG/FV 混合算法和将各种方法统一在一个框架内的CPR (correctionprocedure via reconstruction) 方法等. 随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题, 包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等. 在综述过程中, 介绍了各种方法的优势与不足, 其间介绍了作者发展的基于"静动态混合重构" 的DG/FV 混合算法. 最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.