自适应多重网格有限元网格生成器研制

基于协调三角形剖分算法、分子表数据结构和Ｚｉｅｎｋｉｅｗｉｃｚ－Ｚｈｕ误差估计方法，本文研制出适用于自适应多重网格有限元的网格生成器。该网格生成器可对复杂的区域进行自适应加密。当荷载作用边界随时间变化及在动力荷载作用下，网格生成器可退化与再加密网格。     

Local block refinement with a multigrid flow solver

A local block refinement procedure for the efficient computation of transient incompressible flows with heat transfer is presented. The procedure uses patched structured grids for the blockwise refinement and a parallel multigrid finite volume method with colocated primitive variables to solve the Navier‐Stokes equations. No restriction is imposed on the value of the refinement rate and non‐integer rates may also be used. The procedure is analysed with respect to its sensitivity to the refinement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous significant savings in computing time and memory requirements. Copyright © 2002 John Wiley & Sons, Ltd.     

Patched grid and adaptive mesh refinement strategies for the calculation of the transport of vortices

This paper presents two techniques allowing local grid refinement to calculate the transport of vortices. one is the patched grid (PG) method which allows non‐coincident interfaces between blocks. Treatment of the non‐coincident interfaces is given in detail. The second one is the adaptive mesh refinement (AMR) method which has been developed in order to create embedded sub‐grids. The efficiency of these two methods is demonstrated by some validating tests. Then the PG and AMR strategies are applied in the computation of the transport of vortices. We start with a simple vortex flow in a cubic box. Then, the flowfield around a complex aircraft configuration is calculated using the two refinement techniques. Results are compared with a fine, referenced grid calculation. Copyright © 2002 John Wiley & Sons, Ltd.     

Feature‐based adaptive mesh refinement for wingtip vortices

Feature‐based solution‐adaptive mesh refinement is an attractive strategy when it is known a priori that the resolution of certain key features is critical to achieving the objectives of a simulation. In this paper, we apply vortex characterization techniques, which are typically employed to visualize vortices, to identify regions of the computational domain for mesh refinement. We investigate different refinement strategies that are facilitated by these vortex characterization techniques to simulate the flow past a wing in a wind tunnel. Our results, which we compare with experimental data, indicate that it is necessary to refine the region within and near the vortex extent surface to obtain an accurate prediction. Application of the identified mesh refinement strategy also produced observed improvement in the results predicted for a spinning missile with deflected canards. Copyright © 2010 John Wiley & Sons, Ltd.     

Anisotropic mesh refinement for discontinuous Galerkin methods in two‐dimensional aerodynamic flow simulations

We derive and implement two types of anisotropic indicators which can be used within an anisotropic refinement algorithm for second but also for higher‐order discontinuous Galerkin discretizations. Although the first type of indicator employs the possible inter‐element discontinuities of the discrete functions, the second type of indicator estimates the approximation error in terms of second but possibly also higher‐order derivatives. We implement a simple extension of these indicators to systems of equations which performs similar to the so‐called metric intersection used to combine the metric information of several solution components and is applicable to higher‐order discretizations as well. The anisotropic indicators are incorporated into an adaptive refinement algorithm which uses state‐of‐the‐art residual‐based or adjoint‐based indicators for goal‐oriented refinement to select the elements to be refined, whereas the anisotropic indicators determine which anisotropic case the selected elements shall be refined with. We demonstrate the performance of the anisotropic refinement algorithm for sub‐, trans‐ and supersonic, inviscid and viscous compressible flows around a NACA0012 airfoil. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive mesh refinement and coarsening for aerodynamic flow simulations

A new mesh refinement technique for unstructured grids is discussed. The new technique presents the important advantage of maintaining the original grid skewness, thanks to the capability of handling hanging nodes. The paper also presents an interpretation of MacCormack's method in an unstructured grid context. Results for a transonic convergent–divergent nozzle, for a convergent nozzle with a supersonic entrance and for transonic flow over a NACA 0012 airfoil are presented and discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

Parallel adaptive refinement for unsteady flow calculations on 3D unstructured grids

A parallel adaptive refinement algorithm for three‐dimensional unstructured grids is presented. The algorithm is based on an hierarchical h‐refinement/derefinement scheme for tetrahedral elements.The algorithm has been fully parallelized for shared‐memory platforms via a domain decomposition of the mesh at the algebraic level. The effectiveness of the procedure is demonstrated with applications which involve unsteady compressible fluid flow. A parallel speedup study of the algorithm also is included. Published in 2004 by John Wiley & Sons, Ltd.     

A multiblock/multilevel mesh refinement procedure for CFD computations

A multiblock/multilevel algorithm with local refinement for general two‐ and three‐dimensional fluid flow is presented. The patched‐based local refinement procedure is presented in detail and algorithmic implementations are also presented. The multiblock implementation is essentially block‐unstructured, i.e. each block having its own local curvilinear co‐ordinate system. Refined grid patches can be put anywhere in the computational domain and can extend across block boundaries. To simplify the implementation, while still maintaining sufficient generality, the refinement is restricted to a refinement of the grid successively halving the grid size within a selected patch. The multiblock approach is implemented within the framework of the well‐known SIMPLE solution strategy. Computational experiments showing the effect of using the multilevel solution procedure are presented for a sample elliptic problem and a few benchmark problems of computational fluid dynamics (CFD). Copyright © 2001 John Wiley & Sons, Ltd.     

全自动自适应网格细化

本文利用弹塑性误差估计模型，预示出金属成形数值模拟过程中网格细化时新网格尺寸，提出补角法修正锻件边界构形并利用三次Ｂ样条统一表达边界构形，实现了对边界细化并进而产生自适应细化网格。     

On the performance of adaptive mesh refinement computation

A finite difference scheme for the unsteady Euler equations using an adaptive mesh refinement (AMR) algorithm was applied to the time-dependent flowfield of shock diffraction problems. The effectiveness of the AMR algorithm was evaluated against a uniform mesh algorithm. Computational results showed that to obtain solutions with equivalent resolution, the AMR algorithm requires much less processing time, when compared with a uniform mesh algorithm.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Reordering and incomplete preconditioning in serial and parallel adaptive mesh refinement and coarsening flow solutions

The effects of reordering the unknowns on the convergence of incomplete factorization preconditioned Krylov subspace methods are investigated. Of particular interest is the resulting preconditioned iterative solver behavior when adaptive mesh refinement and coarsening (AMR/C) are utilized for serial or distributed parallel simulations. As representative schemes, we consider the familiar reverse Cuthill–McKee and quotient minimum degree algorithms applied with incomplete factorization preconditioners to CG and GMRES solvers. In the parallel distributed case, reordering is applied to local subdomains for block ILU preconditioning, and subdomains are repartitioned dynamically as mesh adaptation proceeds. Numerical studies for representative applications are conducted using the object‐oriented AMR/C software system libMesh linked to the PETSc solver library. Serial tests demonstrate that global unknown reordering and incomplete factorization preconditioning can reduce the number of iterations and improve serial CPU time in AMR/C computations. Parallel experiments indicate that local reordering for subdomain block preconditioning associated with dynamic repartitioning because of AMR/C leads to an overall reduction in processing time. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite volume adaptive solutions using SIMPLE as smoother

This paper describes a new multilevel procedure that can solve the discrete Navier–Stokes system arising from finite volume discretizations on composite grids, which may consist of more than one level. SIMPLE is used and tested as the smoother, but the multilevel procedure is such that it does not exclude the use of other smoothers. Local refinement is guided by a criterion based on an estimate of the truncation error. The numerical experiments presented test not only the behaviour of the multilevel algebraic solver, but also the efficiency of local refinement based on this particular criterion. Copyright © 2006 John Wiley & Sons, Ltd.     

Evaluation of adaptive mesh refinement and coarsening for the computation of compressible flows on unstructured meshes

The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

三维有限元六面体网格几何自适应再生成方法

基于几何自适应的六面体网再生成方法,提出了一种以栅格法为基本方法,对有限元网格再划分过程中的网格再划分标准、几何形状的获取以及新旧网格之间物理量的传递等关键问题进行了研究.重点介绍了基于几何自适应的六面体网格再生成算法,首先对旧网格实体模型进行识别,根据实体模型几何特征建立加密源点信息场;然后采用栅格法生成核心网格并对...     

Accurate and robust adaptive mesh refinement for aerodynamic simulation with multi‐block structured curvilinear mesh

A multi‐block curvilinear mesh‐based adaptive mesh refinement (AMR) method is developed to satisfy the competing objectives of improving accuracy and reducing cost. Body‐fitted curvilinear mesh‐based AMR is used to capture flow details of various length scales. A series of efforts are made to guarantee the accuracy and robustness of the AMR system. A physics‐based refinement function is proposed, which is proved to be able to detect both shock wave and vortical flow. The curvilinear mesh is refined with cubic interpolation, which guarantees the aspect ratio and smoothness. Furthermore, to enable its application in complex configurations, a sub‐block‐based refinement strategy is developed to avoid generating invalid mesh, which is the consequence of non‐smooth mesh lines or singular geometry features. A newfound problem of smaller wall distance, which negatively affects the stability and is never reported in the literature, is also discussed in detail, and an improved strategy is proposed. Together with the high‐accuracy numerical scheme, a multi‐block curvilinear mesh‐based AMR system is developed. With a series of test cases, the current method is verified to be accurate and robust and be able to automatically capture the flow details at great cost saving compared with the global refinement. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement

A novel numerical scheme is developed by coupling the level set method with the adaptive mesh refinement in order to analyse moving interfaces economically and accurately. The finite element method (FEM) is used to discretize the governing equations with the generalized simplified marker and cell (GSMAC) scheme, and the cubic interpolated pseudo‐particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh refinement is implemented in the quadrangular grid systems and easily embedded in the FEM‐based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two‐dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its effectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni effect is first simulated efficiently with the present scheme. Copyright © 2004 John Wiley & Sons, Ltd.     

Block-based adaptive mesh refinement scheme using numerical density of entropy production for three-dimensional two-fluid flows

In this work, we present a fast and parallel finite volume scheme on unstructured meshes applied to complex fluid flow. The mathematical model is based on a three-dimensional compressible low Mach two-phase flows model, combined with a linearised ‘artificial pressure’ law. This hyperbolic system of conservation laws allows an explicit scheme, improved by a block-based adaptive mesh refinement scheme. Following a previous one-dimensional work, the useful numerical density of entropy production is used as mesh refinement criterion. Moreover, the computational time is preserved using a local time-stepping method. Finally, we show through several test cases the efficiency of the present scheme on two- and three-dimensional dam-break problems over an obstacle.     

Adaptive mesh refinement for high‐resolution finite element schemes

New a posteriori error indicators based on edgewise slope‐limiting are presented. The L₂‐norm is employed to measure the error of the solution gradient in both global and element sense. A second‐order Newton–Cotes formula is utilized in order to decompose the local gradient error from a ??₁ finite element solution into a sum of edge contributions. The slope values at edge midpoints are interpolated from the two adjacent vertices. Traditional techniques to recover (superconvergent) nodal gradient values from consistent finite element slopes are reviewed. The deficiencies of standard smoothing procedures—L₂‐projection and the Zienkiewicz–Zhu patch recovery—as applied to nonsmooth solutions are illustrated for simple academic configurations. The recovered gradient values are corrected by applying a slope limiter edge‐by‐edge so as to satisfy geometric constraints. The direct computation of slopes at edge midpoints by means of limited averaging of adjacent gradient values is proposed as an inexpensive alternative. Numerical tests for various solution profiles in one and two space dimensions are presented to demonstrate the potential of this postprocessing procedure as an error indicator. Finally, it is used to perform adaptive mesh refinement for compressible inviscid flow simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

On some variational acceleration techniques and related methods for local refinement

This paper shows that the well-known variational acceleration method described by Wachspress (E. Wachspress, Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall, Englewood Cliffs, NJ, 1966) and later generalized to multilevels (known as the additive correction multigrid method (B.R Huthchinson and G.D. Raithby, Numer. Heat Transf., 9 , 511–537 (1986))) is similar to the FAC method of McCormick and Thomas (S.F McCormick and J.W. Thomas, Math. Comput., 46 , 439–456 (1986)) and related multilevel methods. The performance of the method is demonstrated for some simple model problems using local refinement and suggestions for improving the performance of the method are given. © 1998 John Wiley & Sons, Ltd.     

Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement

Abstract. Two-dimensional numerical simulations of detonations in two-phase lean mixtures of aluminum particles and pure oxygen have been performed. The computational procedure adopts an adaptive mesh refinement methodology in order to increase spatial resolution in the most interesting parts of the flow field. A one-step heterogeneous reaction describes the evaporation and combustion of aluminum. Depending on the gas-phase temperature, the combustion product is aluminum oxide or aluminum monoxide. The results show that the heterogeneous detonations resemble gaseous single-phase ones although the scale of the phenomena is very different. The detonation of aluminum dust evolves into the 2-headed mode of propagation with the characteristic detonation cell width equal to cm. For aluminum dust the cellular structure is much finer. The detonation initially propagates in the 11-headed mode with the characteristic cell width equal to cm and evolves into the 8.5-headed mode with the characteristic cell size $\lambda_{\rm cell}$ equal to cm. Received 7 May 2001 / Accepted 25 March 2002 Published online 23 January 2003 Correspondence to: K. Benkiewicz (e-mail: kbenk@cow.me.aoyama.ac.jp)