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High-order discontinuous Galerkin solver on hybrid anisotropic meshes for laminar and turbulent simulations 被引量:2
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作者 姜振华 阎超 于剑 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第7期799-812,共14页
Efficient and robust solution strategies are developed for discontinuous Galerkin (DG) discretization of the Navier-Stokes (NS) and Reynolds-averaged NS (RANS) equations on structured/unstructured hybrid meshes.... Efficient and robust solution strategies are developed for discontinuous Galerkin (DG) discretization of the Navier-Stokes (NS) and Reynolds-averaged NS (RANS) equations on structured/unstructured hybrid meshes. A novel line-implicit scheme is devised and implemented to reduce the memory gain and improve the computational eificiency for highly anisotropic meshes. A simple and effective technique to use the mod- ified Baldwin-Lomax (BL) model on the unstructured meshes for the DC methods is proposed. The compact Hermite weighted essentially non-oscillatory (HWENO) limiters are also investigated for the hybrid meshes to treat solution discontinuities. A variety of compressible viscous flows are performed to examine the capability of the present high- order DG solver. Numerical results indicate that the designed line-implicit algorithms exhibit weak dependence on the cell aspect-ratio as well as the discretization order. The accuracy and robustness of the proposed approaches are demonstrated by capturing com- plex flow structures and giving reliable predictions of benchmark turbulent problems. 展开更多
关键词 discontinuous galerkin (DG) method implicit method Baldwin-Lomax(BL) model high order accuracy structured/unstructured hybrid mesh
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A Stable Numerical Scheme Based on the Hybridized Discontinuous Galerkin Method for the Ito-Type Coupled KdV System
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作者 Shima Baharlouei Reza Mokhtari Nabi Chegini 《Communications on Applied Mathematics and Computation》 2022年第4期1351-1373,共23页
The purpose of this paper is to develop a hybridized discontinuous Galerkin(HDG)method for solving the Ito-type coupled KdV system.In fact,we use the HDG method for discre-tizing the space variable and the backward Eu... The purpose of this paper is to develop a hybridized discontinuous Galerkin(HDG)method for solving the Ito-type coupled KdV system.In fact,we use the HDG method for discre-tizing the space variable and the backward Euler explicit method for the time variable.To linearize the system,the time-lagging approach is also applied.The numerical stability of the method in the sense of the L2 norm is proved using the energy method under certain assumptions on the stabilization parameters for periodic or homogeneous Dirichlet bound-ary conditions.Numerical experiments confirm that the HDG method is capable of solving the system efficiently.It is observed that the best possible rate of convergence is achieved by the HDG method.Also,it is being illustrated numerically that the corresponding con-servation laws are satisfied for the approximate solutions of the Ito-type coupled KdV sys-tem.Thanks to the numerical experiments,it is verified that the HDG method could be more efficient than the LDG method for solving some Ito-type coupled KdV systems by comparing the corresponding computational costs and orders of convergence. 展开更多
关键词 hybridized discontinuous galerkin(hdg)method Stability analysis Ito-type coupled KdV system Conservation laws
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High-Order Discontinuous Galerkin Solution of Compressible Flows with a Hybrid Lattice Boltzmann Flux
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作者 Sun Yongcheng Cai Junwei Qin Wanglong 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2018年第3期413-422,共10页
A discontinuous Galerkin(DG)-based lattice Boltzmann method is employed to solve the Euler and Navier-Stokes equations.Instead of adopting the widely used local Lax-Friedrichs flux and Roe Flux etc.,a hybrid lattice B... A discontinuous Galerkin(DG)-based lattice Boltzmann method is employed to solve the Euler and Navier-Stokes equations.Instead of adopting the widely used local Lax-Friedrichs flux and Roe Flux etc.,a hybrid lattice Boltzmann flux solver(LBFS)is employed to evaluate the inviscid flux across the cell interfaces.The main advantage of the hybrid LBFS is its flexibility for capturing both strong shocks and thin boundary layers through introducing a function which varies from zero to one to control the artificial viscosity.Numerical results indicate that the hybrid lattice Boltzmann flux solver behaves very well combining with the high-order DG method when simulating both inviscid and viscous flows. 展开更多
关键词 hybrid lattice Boltzmann flux solver discontinuous galerkin(DG)method Euler equations Navier-Stokes equations
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Superconvergent Interpolatory HDG Methods for Reaction Difusion Equations II:HHO‑Inspired Methods
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作者 Gang Chen Bernardo Cockburn +1 位作者 John R.Singler Yangwen Zhang 《Communications on Applied Mathematics and Computation》 2022年第2期477-499,共23页
In Chen et al.(J.Sci.Comput.81(3):2188–2212,2019),we considered a superconvergent hybridizable discontinuous Galerkin(HDG)method,defned on simplicial meshes,for scalar reaction-difusion equations and showed how to de... In Chen et al.(J.Sci.Comput.81(3):2188–2212,2019),we considered a superconvergent hybridizable discontinuous Galerkin(HDG)method,defned on simplicial meshes,for scalar reaction-difusion equations and showed how to defne an interpolatory version which maintained its convergence properties.The interpolatory approach uses a locally postprocessed approximate solution to evaluate the nonlinear term,and assembles all HDG matrices once before the time integration leading to a reduction in computational cost.The resulting method displays a superconvergent rate for the solution for polynomial degree k≥1.In this work,we take advantage of the link found between the HDG and the hybrid high-order(HHO)methods,in Cockburn et al.(ESAIM Math.Model.Numer.Anal.50(3):635–650,2016)and extend this idea to the new,HHO-inspired HDG methods,defned on meshes made of general polyhedral elements,uncovered therein.For meshes made of shape-regular polyhedral elements afne-equivalent to a fnite number of reference elements,we prove that the resulting interpolatory HDG methods converge at the same rate as for the linear elliptic problems.Hence,we obtain superconvergent methods for k≥0 by some methods.We thus maintain the superconvergence properties of the original methods.We present numerical results to illustrate the convergence theory. 展开更多
关键词 hybrid high-order methods hybridizable discontinuous galerkin methods Interpolatory method SUPERCONVERGENCE
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daptive Hybridized Interior Penalty Discontinuous Galerkin Methods for H(curl)-Elliptic Problems 被引量:1
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作者 C.Carstensen R.H.W.Hoppe +1 位作者 N.Sharma T.Warburton 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2011年第1期13-37,共25页
We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin(IPDG-H)method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents equ... We develop and analyze an adaptive hybridized Interior Penalty Discontinuous Galerkin(IPDG-H)method for H(curl)-elliptic boundary value problems in 2D or 3D arising from a semi-discretization of the eddy currents equations.The method can be derived from a mixed formulation of the given boundary value problem and involves a Lagrange multiplier that is an approximation of the tangential traces of the primal variable on the interfaces of the underlying triangulation of the computational domain.It is shown that the IPDG-H technique can be equivalently formulated and thus implemented as a mortar method.The mesh adaptation is based on a residual-type a posteriori error estimator consisting of element and face residuals.Within a unified framework for adaptive finite element methods,we prove the reliability of the estimator up to a consistency error.The performance of the adaptive symmetric IPDG-H method is documented by numerical results for representative test examples in 2D. 展开更多
关键词 Adaptive hybridized Interior Penalty discontinuous galerkin method a posteriori error analysis H(curl)-elliptic boundary value problems semi-discrete eddy currents equations
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基于非结构/混合网格的高阶精度DG/FV混合方法研究进展 被引量:6
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作者 张来平 李明 +2 位作者 刘伟 赫新 张涵信 《空气动力学学报》 CSCD 北大核心 2014年第6期717-726,共10页
DG/FV 混合方法因其具有紧致、易于推广获得高阶格式及相比同阶精度 DG 方法计算量、存储量小等优点,自提出以来已成功应用于一维、二维标量方程和 Euler/N-S 方程的求解。综述了 DG/FV 混合方法的研究进展,重点介绍了 DG/FV 混... DG/FV 混合方法因其具有紧致、易于推广获得高阶格式及相比同阶精度 DG 方法计算量、存储量小等优点,自提出以来已成功应用于一维、二维标量方程和 Euler/N-S 方程的求解。综述了 DG/FV 混合方法的研究进展,重点介绍了 DG/FV 混合方法的空间重构算法、针对 RANS 方程的求解方法、隐式时间离散格式、数值色散耗散及稳定性分析、计算量理论分析,并给出了系列粘性流算例的计算结果,包括用于验证混合方法数值精度的库埃特流,以及方腔流、亚声速剪切层、低速平板湍流、NACA0012翼型湍流绕流等。数值计算结果表明 DG/FV 混合方法达到了设计的精度阶,且相比同阶 DG 方法计算量减少约40%,而隐式方法能大幅提高定常流的收敛历程,较显式 Runge-Kutta 的收敛速度提高1~2个量级。 展开更多
关键词 非结构/混合网格 间断 galerkin 方法 有限体积方法 DG/FV 混合方法 RANS 方程
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基于非结构/混合网格的高阶精度格式研究进展 被引量:22
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作者 张来平 贺立新 +2 位作者 刘伟 李明 张涵信 《力学进展》 EI CSCD 北大核心 2013年第2期202-236,共35页
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... 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(correction procedure 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. 展开更多
关键词 非结构网格 混合网格 高阶精度格式 有限体积方法 间断伽辽金方法 有限谱体积方法 有限谱差分方法 DG FV混合算法
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基于静动态混合重构的DG/FV混合格式 被引量:5
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作者 张来平 刘伟 +1 位作者 贺立新 邓小刚 《力学学报》 EI CSCD 北大核心 2010年第6期1013-1022,共10页
通过比较紧致格式和间断Galerkin(DG)格式,提出了"静态重构"和"动态重构"的概念,对有限体积方法和DG有限元方法进行统一的表述.借鉴有限体积的思想,发展了基于"混合重构"技术的一类新的DG格式,称之为间断... 通过比较紧致格式和间断Galerkin(DG)格式,提出了"静态重构"和"动态重构"的概念,对有限体积方法和DG有限元方法进行统一的表述.借鉴有限体积的思想,发展了基于"混合重构"技术的一类新的DG格式,称之为间断Galerkin有限元/有限体积混合格式(DG/FV格式).该类混合格式通过适当地扩展模板(拓展至紧邻单元)重构单元内的高阶多项式分布,在提高精度的同时,减少了传统DG格式的计算量和存储量.通过典型一维和二维标量方程的计算发现新的混合格式在有些情况下具有超收敛(superconvergence)性质. 展开更多
关键词 DG有限元法 有限体积法 静态重构 动态重构 混合格式
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基于静动态重构的高阶DG/FV混合格式在二维非结构网格中的推广 被引量:3
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作者 张来平 刘伟 +2 位作者 贺立新 赫新 邓小刚 《计算物理》 EI CSCD 北大核心 2011年第2期188-198,共11页
通过比较间断Galerkin有限元方法(DGM)和有限体积方法(FVM),提出"静态重构"和"动态重构"的概念,进一步建立基于静动态"混合重构"算法的三阶DG/FV混合格式.在DG/FV混合格式中,单元平均值和一阶导数由DGM方... 通过比较间断Galerkin有限元方法(DGM)和有限体积方法(FVM),提出"静态重构"和"动态重构"的概念,进一步建立基于静动态"混合重构"算法的三阶DG/FV混合格式.在DG/FV混合格式中,单元平均值和一阶导数由DGM方法"动态重构",二阶导数利用FVM方法"静态重构";在此基础上,构造高阶多项式插值函数,得到三阶精度的DG/FV混合格式.将DG/FV混合格式推广应用于二维非结构网格,求解二维标量方程和Euler方程.典型算例数值实验表明,DG/FV混合格式达到了理想中的三阶精度. 展开更多
关键词 DG有限元法 有限体积法 Taylor基 混合格式 非结构网格
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高阶精度 DG/FV 混合方法在二维粘性流动模拟中的推广 被引量:2
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作者 李明 刘伟 +1 位作者 张来平 张涵信 《空气动力学学报》 CSCD 北大核心 2015年第1期17-24,30,共9页
DG/FV 混合方法因其具有紧致性、易于推广至高阶及相比同阶 DGM 计算量、存储量小等优点,已成功应用于一维/二维标量方程和 Euler 方程的求解。在此基础上,将该方法推广于二维三角形/矩形混合网格上的 Navier-Stokes 方程数值模拟... DG/FV 混合方法因其具有紧致性、易于推广至高阶及相比同阶 DGM 计算量、存储量小等优点,已成功应用于一维/二维标量方程和 Euler 方程的求解。在此基础上,将该方法推广于二维三角形/矩形混合网格上的 Navier-Stokes 方程数值模拟,将格式形式精度提高至4~5阶。物理量的空间重构及离散使用 DG/FV 混合重构方法;无粘通量计算采用 Roe 格式;粘性通量计算采用 BR2格式;时间方向离散采用高阶显式 R-K 方法或隐式方法。利用该方法计算了有解析解的 Couette 流动问题以验证几种格式的数值精度阶,并计算了层流平板流动和定常、非定常圆柱绕流问题等经典算例。计算结果表明 DG/FV 混合方法达到了设计的精度阶,在较粗的网格上亦能得到高精度的计算结果;定性分析和数值结果表明相比同阶 DG 方法单步计算量减少约40%。 展开更多
关键词 非结构/混合网格 间断 galerkin 方法 有限体积方法 DG/FV 混合方法 Navier-Stokes 方程
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基于非结构/混合网格模拟黏性流的高阶精度DDG/FV混合方法 被引量:6
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作者 邵帅 李明 +1 位作者 王年华 张来平 《力学学报》 EI CSCD 北大核心 2018年第6期1470-1482,共13页
间断Galerkin有限元方法 (discontinuous Galerkin method, DGM)因具有计算精度高、模板紧致、易于并行等优点,近年来已成为非结构/混合网格上广泛研究的高阶精度数值方法.但其计算量和内存需求量巨大,特别是对于网格规模达到百万甚至... 间断Galerkin有限元方法 (discontinuous Galerkin method, DGM)因具有计算精度高、模板紧致、易于并行等优点,近年来已成为非结构/混合网格上广泛研究的高阶精度数值方法.但其计算量和内存需求量巨大,特别是对于网格规模达到百万甚至数千万的大型三维实际复杂外形问题,其计算量和存储量对计算资源的消耗是难以承受的.基于"混合重构"的DG/FV格式可以有效降低DGM的计算量和存储量.本文将DDG黏性项离散方法推广应用于DG/FV混合算法,得到新的DDG/FV混合格式,以进一步提高DG/FV混合算法对于黏性流动模拟的计算效率.通过Couette流动、层流平板边界层、定常圆柱绕流,非定常圆柱绕流和NACA0012翼型绕流等二维黏性流算例,优化了DDG通量公式中的参数选择,验证了DDG/FV混合格式对定常和非定常黏性流模拟的精度和计算效率,并与广泛使用的BR2-DG格式的计算结果和效率进行对比研究.一系列数值实验结果表明,本文构造的DDG/FV混合格式在二维非结构/混合网格的Navier-Stokes方程求解中,在达到相同的数值精度阶的前提下,相比BR2-DG格式,对于隐式时间离散的定常问题计算效率提高了2倍以上,对于显式时间离散的非定常问题计算效率提高1.6倍,并且在一些算例中,混合格式具有更优良的计算稳定性.DDG/FV混合格式提升了计算效率和稳定性,具有良好的应用前景. 展开更多
关键词 直接间断迦辽金方法DDG DG/FV混合算法 高阶精度数值方法 非结构/混合网格
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基于混合网格的高阶间断有限元黏流数值解法 被引量:7
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作者 秦望龙 吕宏强 伍贻兆 《力学学报》 EI CSCD 北大核心 2013年第6期987-991,共5页
针对层流NS方程发展了混合网格上的高阶间断有限元方法,给出了物面边界高阶近似的具体步骤以及近物面弯曲单元的处理方法.对数值离散产生的非线性方程组采用牛顿迭代进行求解,每个牛顿循环采用预处理广义最小余量法求解产生的大型稀疏... 针对层流NS方程发展了混合网格上的高阶间断有限元方法,给出了物面边界高阶近似的具体步骤以及近物面弯曲单元的处理方法.对数值离散产生的非线性方程组采用牛顿迭代进行求解,每个牛顿循环采用预处理广义最小余量法求解产生的大型稀疏线性系统.使用该方法得到了典型算例的数值结果,并跟前人的计算结果进行了比较.计算结果表明,混合网格上应用高阶间断有限元方法求解黏性流动具有很好的应用前景. 展开更多
关键词 混合网格 高阶间断有限元 物面高阶近似 层流
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改进的二维三维混合时域不连续伽辽金方法 被引量:2
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作者 买文鼎 郝文曲 +2 位作者 李平 刘露 胡俊 《电波科学学报》 EI CSCD 北大核心 2018年第1期33-40,共8页
对高速信号通过电源板时的电源完整性(power integrity,PI)问题进行研究时,因为电源板中主要模式分布为零阶平行板模式,可以采用二维简化以提高效率.而对于隔离盘或其它存在纵向不连续性的区域,则应采用三维算法以保证精度.将两者结合... 对高速信号通过电源板时的电源完整性(power integrity,PI)问题进行研究时,因为电源板中主要模式分布为零阶平行板模式,可以采用二维简化以提高效率.而对于隔离盘或其它存在纵向不连续性的区域,则应采用三维算法以保证精度.将两者结合起来的一种二维三维(2D/3D)混合时域不连续伽辽金(discontinuous Galerkin time domain,DGTD)方法可以兼顾精度与效率,有效地处理这类电磁全波计算问题.其中二维、三维方法采用同一套三棱柱离散的网格,通过适当设置基函数,二维区域与二维区域之间可以方便快速地相互转化.随着电磁波的传播,二维、三维的适用区域是随时间、空间动态变化的.为了准确地捕捉这种动态变化,文中提出的一种改进的自适应判据,在每个时间歩对电磁场进行检测,从而动态地判定二维简化区域.与现有技术的判据控制绝对误差不同,该方法对相对误差进行控制,效率高、精度好,对于不同的结构适应性强.通过数值实验,与商业软件和全三维(3D)DGTD方法的结果进行了比较和验证. 展开更多
关键词 二维三维混合 自适应判据 时域不连续伽辽金 区域分解 模式分解 误差控制 电源完整性 电源板 导孔建模
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基于混合重构高阶间断伽辽金方法的二维层流和湍流数值模拟 被引量:1
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作者 熊为 张卫国 +2 位作者 丁珏 杨小权 翁培奋 《上海大学学报(自然科学版)》 CAS CSCD 北大核心 2022年第4期608-620,共13页
为了提高间断伽辽金方法的计算效率,解决least-squares重构方法无法满足2-exact的缺陷,发展了基于recovery重构和least-squares重构相结合的三阶混合重构方法,用于求解可压缩层流和湍流流动.将Navier-Stokes方程和修正的一方程Negative ... 为了提高间断伽辽金方法的计算效率,解决least-squares重构方法无法满足2-exact的缺陷,发展了基于recovery重构和least-squares重构相结合的三阶混合重构方法,用于求解可压缩层流和湍流流动.将Navier-Stokes方程和修正的一方程Negative Spalart-Allmaras模型方程耦合成为系统方程,采用三阶重构间断伽辽金方法进行求解.时间推进采用基于半解析精确Jacobian矩阵的上-下对称高斯赛德尔格式(lower-upper symmetric Gauss-Seidel scheme,LU-SGS)预处理广义极小剩余(generalized minimal residual,GMRES)方法和四阶隐式Runge-Kutta方法;空间对流项离散采用Haten-Lax-van Leer接触(Haten-Lax-van Leer contact,HLLC)格式;黏性项离散采用第二Bassi-Rebay(second Bassi-Rebay,BR2)格式,并对BR2局部和全局提升算子开展三阶重构,达到提高计算精度的目的.通过典型算例验证了发展rDGP_(1)P_(2)方法的准确性和计算效率.研究结果表明:重构的rDGP_(1)P_(2)方法不仅具有较高的计算精度,而且还具有较高的计算效率. 展开更多
关键词 高阶精度 间断伽辽金方法 混合重构 第二Bassi-Rebay(second Bassi-Rebay BR2)格式
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二维间断有限元混合网格混合算法研究
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作者 张冬云 杨永 +1 位作者 郭永恒 李喜乐 《航空计算技术》 2009年第1期64-67,共4页
针对二维流场进行结构/非结构混合网格划分,在靠近物面处生成结构化网格,在结构化网格以外和远场之间以非结构化网格填充。使用间断有限元方法(DGM)离散Eu ler方程。在混合网格混合算法中,结构化网格区域使用结构DGM,非结构化网格区域... 针对二维流场进行结构/非结构混合网格划分,在靠近物面处生成结构化网格,在结构化网格以外和远场之间以非结构化网格填充。使用间断有限元方法(DGM)离散Eu ler方程。在混合网格混合算法中,结构化网格区域使用结构DGM,非结构化网格区域使用非结构DGM,保证结构/非结构对接面处的通量守恒,并加入moment限制器消除激波前后伪震荡。对NACA0012和RAE 2822翼型跨音速无粘流动的数值模拟结果说明了混合算法的有效性以及在捕捉间断方面的能力。 展开更多
关键词 混合网格混合算法 间断有限元方法 moment限制器
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UNIFORM STABILITY AND ERROR ANALYSIS FOR SOME DISCONTINUOUS GALERKIN METHODS 被引量:1
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作者 Qingguo Hong Jinchao Xu 《Journal of Computational Mathematics》 SCIE CSCD 2021年第2期283-310,共28页
In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefu... In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method. 展开更多
关键词 Uniform Stability Uniform Error Estimate hybrid discontinuous galerkin Weak galerkin
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p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with Static Condensation
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作者 Lorenzo Botti Daniele A.Di Pietro 《Communications on Applied Mathematics and Computation》 2022年第3期783-822,共40页
We propose a p-multilevel preconditioner for hybrid high-order(HHO)discretizations of the Stokes equation,numerically assess its performance on two variants of the method,and compare with a classical discontinuous Gal... We propose a p-multilevel preconditioner for hybrid high-order(HHO)discretizations of the Stokes equation,numerically assess its performance on two variants of the method,and compare with a classical discontinuous Galerkin scheme.An efficient implementa-tion is proposed where coarse level operators are inherited using L2-orthogonal projec-tions defined over mesh faces and the restriction of the fine grid operators is performed recursively and matrix-free.Both h-and k-dependency are investigated tackling two-and three-dimensional problems on standard meshes and graded meshes.For the two HHO for-mulations,featuring discontinuous or hybrid pressure,we study how the combination of p-coarsening and static condensation influences the V-cycle iteration.In particular,two dif-ferent static condensation procedures are considered for the discontinuous pressure HHO variant,resulting in global linear systems with a different number of unknowns and matrix non-zero entries.Interestingly,we show that the efficiency of the solution strategy might be impacted by static condensation options in the case of graded meshes. 展开更多
关键词 Stokes equations Divergence free constraint hybrid high-order discontinuous galerkin P-MULTIGRID Static condensation
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Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations
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作者 Haiyang Gao Z.J.Wang H.T.Huynh 《Communications in Computational Physics》 SCIE 2013年第4期1013-1044,共32页
A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via recons... A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via reconstruction).The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure.In addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral difference.To discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous approaches.The first three of these approaches,originally derived using the integral formulation,were recast here in the CPR framework,whereas the I-continuous scheme,originally derived for a quadrilateral mesh,was extended to a triangular mesh.Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out.Finally,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach. 展开更多
关键词 discontinuous galerkin lifting collocation penalty flux reconstruction Navier-Stokes equations correction procedure via reconstruction unstructured hybrid grids
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Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations
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作者 Weixiong Yuan Tiegang Liu +2 位作者 Bin Zhang Kui Cao Kun Wang 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2024年第1期1-36,共36页
A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling mode... A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost. 展开更多
关键词 Direct discontinuous galerkin central difference schemes multidomain hybrid methods viscous terms hyperbolic-parabolic equations
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A GENERAL HIGH-ORDER MULTI-DOMAIN HYBRID DG/WENO-FD METHOD FOR HYPERBOLIC CONSERVATION LAWS 被引量:2
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作者 Jian Cheng Kun Wang Tiegang Liu 《Journal of Computational Mathematics》 SCIE CSCD 2016年第1期30-48,共19页
In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order (p ≥ 3) DG method and a q^th-order (q ≥ 3) WENO-FD scheme, is developed. There are two possible coupling appr... In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order (p ≥ 3) DG method and a q^th-order (q ≥ 3) WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative error is proved to be upmost third order. As for the conservative coupling approach, accuracy analysis shows the forced conservation strategy at the coupling interface deteriorates the accuracy locally to first- order accuracy at the 'coupling cell'. A numerical experiments of numerical stability is also presented for the non-conservative and conservative coupling approaches. Several numerical results are presented to verify the theoretical analysis results and demonstrate the performance of the hybrid DG/WENO-FD solver. 展开更多
关键词 discontinuous galerkin method Weighted essentially nonoscillatory scheme hybrid methods high-order scheme.
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