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Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows
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作者 Lan JIANG Jie WU +1 位作者 Liming YANG Hao DONG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第6期961-980,共20页
A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined wit... A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy. 展开更多
关键词 circular function-based gas kinetic flux solver(C-GKFS) weighted essentially non-oscillatory(weno)scheme compressible flow finite volume method
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Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations
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作者 Zachary M.Miksis Yong-Tao Zhang 《Communications on Applied Mathematics and Computation》 EI 2024年第1期3-29,共27页
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of ... Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids. 展开更多
关键词 Fixed-point fast sweeping methods weighted essentially non-oscillatory(weno)schemes Sparse grids Static Hamilton-Jacobi(H-J)equations Eikonal equations
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Efficient Sparse-Grid Implementation of a Fifth-Order Multi-resolution WENO Scheme for Hyperbolic Equations
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作者 Ernie Tsybulnik Xiaozhi Zhu Yong-Tao Zhang 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1339-1364,共26页
High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of th... High-order accurate weighted essentially non-oscillatory(WENO)schemes are a class of broadly applied numerical methods for solving hyperbolic partial differential equations(PDEs).Due to highly nonlinear property of the WENO algorithm,large amount of computational costs are required for solving multidimensional problems.In our previous work(Lu et al.in Pure Appl Math Q 14:57–86,2018;Zhu and Zhang in J Sci Comput 87:44,2021),sparse-grid techniques were applied to the classical finite difference WENO schemes in solving multidimensional hyperbolic equations,and it was shown that significant CPU times were saved,while both accuracy and stability of the classical WENO schemes were maintained for computations on sparse grids.In this technical note,we apply the approach to recently developed finite difference multi-resolution WENO scheme specifically the fifth-order scheme,which has very interesting properties such as its simplicity in linear weights’construction over a classical WENO scheme.Numerical experiments on solving high dimensional hyperbolic equations including Vlasov based kinetic problems are performed to demonstrate that the sparse-grid computations achieve large savings of CPU times,and at the same time preserve comparable accuracy and resolution with those on corresponding regular single grids. 展开更多
关键词 weighted essentially non-oscillatory(weno)schemes Multi-resolution weno schemes Sparse grids High spatial dimensions Hyperbolic partial differential equations(PDEs)
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Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme 被引量:1
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作者 Li Chen Guo Qilong +1 位作者 Li Qin Zhang Hanxin 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2017年第5期524-534,共11页
A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achieveme... A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions. 展开更多
关键词 hypersonic flows shock wave/boundary layer interactions weighted essentially non-oscillatory(weno)scheme slip boundary conditions
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Quinpi:Integrating Conservation Laws with CWENO Implicit Methods
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作者 G.Puppo M.Semplice G.Visconti 《Communications on Applied Mathematics and Computation》 2023年第1期343-369,共27页
Many interesting applications of hyperbolic systems of equations are stiff,and require the time step to satisfy restrictive stability conditions.One way to avoid small time steps is to use implicit time integration.Im... Many interesting applications of hyperbolic systems of equations are stiff,and require the time step to satisfy restrictive stability conditions.One way to avoid small time steps is to use implicit time integration.Implicit integration is quite straightforward for first-order schemes.High order schemes instead also need to control spurious oscillations,which requires limiting in space and time also in the linear case.We propose a framework to simplify considerably the application of high order non-oscillatory schemes through the introduction of a low order implicit predictor,which is used both to set up the nonlinear weights of a standard high order space reconstruction,and to achieve limiting in time.In this preliminary work,we concentrate on the case of a third-order scheme,based on diagonally implicit Runge Kutta(DIRK)integration in time and central weighted essentially non-oscillatory(CWENO)reconstruction in space.The numerical tests involve linear and nonlinear scalar conservation laws. 展开更多
关键词 Implicit schemes essentially non-oscillatory schemes Finite volumes weno and Cweno reconstructions
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Interface flux reconstruction method based on optimized weight essentially non-oscillatory scheme 被引量:4
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作者 Peixun YU Junqiang BAI +2 位作者 Hai YANG Song CHEN Kai PAN 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第5期1020-1029,共10页
Aimed at the computational aeroacoustics multi-scale problem of complex configurations discretized with multi-size mesh, the flux reconstruction method based on modified Weight Essentially Non-Oscillatory(WENO) sche... Aimed at the computational aeroacoustics multi-scale problem of complex configurations discretized with multi-size mesh, the flux reconstruction method based on modified Weight Essentially Non-Oscillatory(WENO) scheme is proposed at the interfaces of multi-block grids.With the idea of Dispersion-Relation-Preserving(DRP) scheme, different weight coefficients are obtained by optimization, so that it is in WENO schemes with various characteristics of dispersion and dissipation. On the basis, hybrid flux vector splitting method is utilized to intelligently judge the amplitude of the gap between grid interfaces. After the simulation and analysis of 1D convection equation with different initial conditions, modified WENO scheme is proved to be able to independently distinguish the gap amplitude and generate corresponding dissipation according to the grid resolution. Using the idea of flux reconstruction at grid interfaces, modified WENO scheme with increasing dissipation is applied at grid points, while DRP scheme with low dispersion and dissipation is applied at the inner part of grids. Moreover, Gauss impulse spread and periodic point sound source flow among three cylinders with multi-scale grids are carried out. The results show that the flux reconstruction method at grid interfaces is capable of dealing with Computational Aero Acoustics(CAA) multi-scale problems. 展开更多
关键词 Computational aeroacousties Dispersion-Relation-Preserving (DRP) scheme Flux reconstruction Modified weight essentially non-oscillatory (wenoscheme Multi-size mesh
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New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
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作者 Alina Chertock Michael Herty +3 位作者 Arsen S.Iskhakov Safa Janajra Alexander Kurganov Maria Lukacova-Medvid'ova 《Communications on Applied Mathematics and Computation》 EI 2024年第3期2011-2044,共34页
In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume fram... In this paper,we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations(PDEs)with uncertainties.The new approach is realized in the semi-discrete finite-volume framework and is based on fifth-order weighted essentially non-oscillatory(WENO)interpolations in(multidimensional)random space combined with second-order piecewise linear reconstruction in physical space.Compared with spectral approximations in the random space,the presented methods are essentially non-oscillatory as they do not suffer from the Gibbs phenomenon while still achieving high-order accuracy.The new methods are tested on a number of numerical examples for both the Euler equations of gas dynamics and the Saint-Venant system of shallow-water equations.In the latter case,the methods are also proven to be well-balanced and positivity-preserving. 展开更多
关键词 Hyperbolic conservation and balance laws with uncertainties Finite-volume methods Central-upwind schemes weighted essentially non-oscillatory(weno)interpolations
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基于保色散关系的迎风WENO格式的研究
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作者 李文成 封建湖 邓子辰 《西北工业大学学报》 EI CAS CSCD 北大核心 2006年第2期165-169,共5页
W ENO(W eighted E ssentially N on-O scillatory)格式能够高分辨率地捕捉诸如激波等间断,而保色散关系(D issipation-R elation-P reserv ing,DRP)格式适宜于处理高频波传播问题。计算气动声学(Com putational-A eroacoustics,CAA)领... W ENO(W eighted E ssentially N on-O scillatory)格式能够高分辨率地捕捉诸如激波等间断,而保色散关系(D issipation-R elation-P reserv ing,DRP)格式适宜于处理高频波传播问题。计算气动声学(Com putational-A eroacoustics,CAA)领域有大量的既有高频波传播又带有激波的问题,结合W ENO格式和DRP格式的优点基于保色散关系构造出优化的迎风W ENO格式。数值实验中比较该格式捕捉波数的能力和精度,显示处理CAA基本问题具有高精度、高分辨率的特点。 展开更多
关键词 加权本质无振荡格式(weno) 高分辨率 保色散关系 计算气动声学
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高效率的特征型紧致WENO混合格式
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作者 骆信 吴颂平 《北京航空航天大学学报》 EI CAS CSCD 北大核心 2020年第7期1379-1386,共8页
特征型紧致加权基本无振荡(WENO)混合格式HCW-R结合了迎风紧致格式CS5-P和WENO格式,具有十分优异的分辨率特性。但在求解多维方程组时,HCW-R格式需要求解块状三对角方程组,因而计算代价十分高昂。采用迎风紧致格式CS5-F代替CS5-P,构造... 特征型紧致加权基本无振荡(WENO)混合格式HCW-R结合了迎风紧致格式CS5-P和WENO格式,具有十分优异的分辨率特性。但在求解多维方程组时,HCW-R格式需要求解块状三对角方程组,因而计算代价十分高昂。采用迎风紧致格式CS5-F代替CS5-P,构造了一个新的特征型紧致WENO混合格式HCW-E。由于HCW-E的特殊形式,其可沿迎风方向、由边界处向内推进求解,避免了处理三对角或块状三对角方程组,从而其计算代价与显式格式无异。虽然就分辨率而言,HCW-E稍逊于HCW-R,但前者的计算效率要显著高于后者。因此,当花费相同的计算代价,HCW-E格式可以获得更好的数值结果。一系列求解Euler方程组的数值试验验证了HCW-E的高分辨率特性和相比HCW-R更高的计算效率。HCW-E格式的效率优势在求解高维问题时更为明显。 展开更多
关键词 紧致格式 加权基本无振荡(weno)格式 混合格式 高分辨率 激波捕捉
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High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations 被引量:1
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作者 Jie Du Yang Yang 《Communications on Applied Mathematics and Computation》 2023年第1期31-63,共33页
In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical ... In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme. 展开更多
关键词 weighted essentially non-oscillatory scheme Finite difference method Stiff source DETONATIONS Bound-preserving CONSERVATIVE
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The Formulation of Finite Difference RBFWENO Schemes for Hyperbolic Conservation Laws:An Alternative Technique
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作者 Rooholah Abedian Mehdi Dehghan 《Advances in Applied Mathematics and Mechanics》 SCIE 2023年第4期1023-1055,共33页
To solve conservation laws,efficient schemes such as essentially nonoscillatory(ENO)and weighted ENO(WENO)have been introduced to control the Gibbs oscillations.Based on radial basis functions(RBFs)with the classical ... To solve conservation laws,efficient schemes such as essentially nonoscillatory(ENO)and weighted ENO(WENO)have been introduced to control the Gibbs oscillations.Based on radial basis functions(RBFs)with the classical WENO-JS weights,a new type of WENO schemes has been proposed to solve conservation laws[J.Guo et al.,J.Sci.Comput.,70(2017),pp.551–575].The purpose of this paper is to introduce a new formulation of conservative finite difference RBFWENO schemes to solve conservation laws.Unlike the usual method for reconstructing the flux functions,the flux function is generated directly with the conservative variables.Comparing with Guo and Jung(2017),the main advantage of this framework is that arbitrary monotone fluxes can be employed,while in Guo and Jung(2017)only smooth flux splitting can be used to reconstruct flux functions.Several 1D and 2D benchmark problems are prepared to demonstrate the good performance of the new scheme. 展开更多
关键词 weighted essentially non-oscillatory scheme radial basis functions interpolation finite difference method hyperbolic conservation laws
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非平衡流解耦方法及其计算激波诱导燃烧的应用验证 被引量:8
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作者 孙明波 梁剑寒 王振国 《航空动力学报》 EI CAS CSCD 北大核心 2008年第11期2055-2061,共7页
介绍并发展了一种改进的化学非平衡流动解耦方法.将流动控制方程与化学反应生成源项解耦处理,组分对流项的矢通量分裂基于流动方程密度对流项的分裂形式给出.对流项采用五阶WENO格式求解,化学反应源项的刚性采用简化的隐式方法进行处理... 介绍并发展了一种改进的化学非平衡流动解耦方法.将流动控制方程与化学反应生成源项解耦处理,组分对流项的矢通量分裂基于流动方程密度对流项的分裂形式给出.对流项采用五阶WENO格式求解,化学反应源项的刚性采用简化的隐式方法进行处理.将该方法应用于预混H2/O2和H2/Air激波诱导燃烧计算,得到的定常及非定常燃烧过程与实验观测相符,振荡频率与实验测量较吻合,结果表明该方法应用于多组分多步反应流计算是可行的. 展开更多
关键词 激波诱导燃烧 非平衡流 解耦方法 weno格式
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基于加权本质无振荡格式的二维溃坝水流数值模拟 被引量:13
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作者 魏文礼 郭永涛 《水利学报》 EI CSCD 北大核心 2007年第5期596-600,共5页
将加权本质无振荡WENO(Weighted essentially non-oscillatory)格式和Runge-Kutta时间离散的思想应用于二维浅水控制方程的求解中,建立了模拟大坝瞬间全溃或局部溃倒所致的洪水演进过程的数学模型。应用该模型对一维矩形明渠中大坝瞬间... 将加权本质无振荡WENO(Weighted essentially non-oscillatory)格式和Runge-Kutta时间离散的思想应用于二维浅水控制方程的求解中,建立了模拟大坝瞬间全溃或局部溃倒所致的洪水演进过程的数学模型。应用该模型对一维矩形明渠中大坝瞬间全溃所致的水流运动进行了数值计算,并与理论解进行了比较,证实了方法的可靠性。最后用该模型预测了矩形河道中大坝瞬间局部溃倒时的洪水演进过程,模拟结果与实际相符。算例表明采用WENO格式所建立的高分辨率溃坝模型能够很好地模拟溃坝波的演进过程。 展开更多
关键词 weno格式 溃坝 数值模拟
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一种通量加权型紧致格式 被引量:1
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作者 袁湘江 涂国华 +1 位作者 许坦 陆利蓬 《航空动力学报》 EI CAS CSCD 北大核心 2008年第1期64-69,共6页
将通量加权的思想引入到紧致格式中,构造了一个传统方法与紧致格式混合组成的加权型差分格式.利用该格式与二阶TVD格式分别计算了一维方波、组合波问题和一些黎曼问题,如Sod问题和Shu问题,以及一维定常激波问题.计算结果的比较表明加权... 将通量加权的思想引入到紧致格式中,构造了一个传统方法与紧致格式混合组成的加权型差分格式.利用该格式与二阶TVD格式分别计算了一维方波、组合波问题和一些黎曼问题,如Sod问题和Shu问题,以及一维定常激波问题.计算结果的比较表明加权格式无论在捕捉各种间断,还是在分辨各种复杂波系上,都具有较大的优势,并与精确解非常吻合. 展开更多
关键词 航空 航天推进系统 数值方法 迎风紧致格式 通量加权型差分格式
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适于可压缩多尺度流动的紧致型激波捕捉格式 被引量:2
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作者 李彦苏 阎超 于剑 《北京航空航天大学学报》 EI CAS CSCD 北大核心 2017年第8期1602-1609,共8页
针对可压缩多尺度流动数值模拟特点,研究一种五阶高分辨率紧致型激波捕捉格式——紧致重构加权基本无振荡(CRWENO)格式。该格式利用非线性权系数将低阶紧致格式加权组合以达到高阶精度。在光滑区域蜕化成具有高分辨率的五阶线性紧致格式... 针对可压缩多尺度流动数值模拟特点,研究一种五阶高分辨率紧致型激波捕捉格式——紧致重构加权基本无振荡(CRWENO)格式。该格式利用非线性权系数将低阶紧致格式加权组合以达到高阶精度。在光滑区域蜕化成具有高分辨率的五阶线性紧致格式,在间断附近则能保持计算稳定无振荡。对CRWENO格式、目前广泛使用的加权基本无振荡(WENO)格式及两格式对应的线性格式(即五阶线性迎风格式和五阶紧致格式)进行数值性能研究,评估非线性权系数对格式耗散及频谱特性的影响。使用一维、二维、三维典型算例进行数值试验,探讨线性/非线性、紧致/非紧致格式在可压缩多尺度流动模拟中的优势和不足。结果表明,CRWENO格式在强压缩性流场模拟中能够稳定地捕捉激波,其紧致特性则改善了非线性格式普遍存在的耗散过大、分辨率较差的问题,使其能够清晰捕捉多尺度流动结构。因此,该格式在可压缩多尺度流动模拟中具有较大优势。 展开更多
关键词 紧致格式 加权基本无振荡(weno)格式 激波捕捉 数值耗散 频谱特性 可压缩多尺度流动
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Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes 被引量:6
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作者 Yong-Tao Zhang Chi-Wang Shu 《Communications in Computational Physics》 SCIE 2009年第2期836-848,共13页
We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrah... We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes.We use the Lax-Friedrichs monotone flux as building blocks,third order reconstructions made from combinations of linear polynomials which are constructed on diversified small stencils of a tetrahedral mesh,and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials.Numerical examples are given to demonstrate stability and accuracy of the scheme. 展开更多
关键词 weighted essentially non-oscillatory(weno)schemes finite volume schemes highorder accuracy tetrahedral meshes
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On the Positivity of Linear Weights in WENO Approximations 被引量:1
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作者 Yuan-yuan Liu Chi-wang Shu Meng-ping Zhang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第3期503-538,共36页
High order accurate weighted essentially non-oscillatory (WENO) schemes have been used extensively in numerical solutions of hyperbolic partial differential equations and other convection dominated problems. However... High order accurate weighted essentially non-oscillatory (WENO) schemes have been used extensively in numerical solutions of hyperbolic partial differential equations and other convection dominated problems. However the WENO procedure can not be applied directly to obtain a stable scheme when negative linear weights are present. In this paper, we first briefly review the WENO framework and the role of linear weights, and then present a detailed study on the positivity of linear weights in a few typical WENO procedures, including WENO interpolation, WENO reconstruction and WENO approximation to first and second derivatives, and WENO integration. Explicit formulae for the linear weights are also given for these WENO procedures. The results of this paper should be useful for future design of WENO schemes involving interpolation, reconstruction, approximation to first and second derivatives, and integration procedures. 展开更多
关键词 weighted essentially non-oscillatory (weno scheme hyperbolic partial differential equations weno interpolation weno reconstruction weno approximation to derivatives weno integration
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On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes 被引量:2
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作者 Rui Zhang Mengping Zhang Chi-Wang Shu 《Communications in Computational Physics》 SCIE 2011年第3期807-827,共21页
In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory(WENO)schemes in two dimensional Cartesian meshes.We compare them in terms of accuracy,performance for smooth an... In this paper we consider two commonly used classes of finite volume weighted essentially non-oscillatory(WENO)schemes in two dimensional Cartesian meshes.We compare them in terms of accuracy,performance for smooth and shocked solutions,and efficiency in CPU timing.For linear systems both schemes are high order accurate,however for nonlinear systems,analysis and numerical simulation results verify that one of them(Class A)is only second order accurate,while the other(Class B)is high order accurate.The WENO scheme in Class A is easier to implement and costs less than that in Class B.Numerical experiments indicate that the resolution for shocked problems is often comparable for schemes in both classes for the same building blocks and meshes,despite of the difference in their formal order of accuracy.The results in this paper may give some guidance in the application of high order finite volume schemes for simulating shocked flows. 展开更多
关键词 weighted essentially non-oscillatory(weno)schemes finite volume schemes ACCURACY
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Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave 被引量:1
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作者 Tianbao MA Chentao WANG Xiangzhao XU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2022年第3期417-436,共20页
A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens t... A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens the discontinuous solution in the arc-length space.This in turn weakens the singularity of the equation.To avoid constructing a high-order scheme directly in the deformed physical space,the entire calculation process is conducted in a uniform orthogonal arc-length space.Furthermore,to ensure the stability of the equation,the time step is reduced by limiting the moving speed of the mesh.Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves,it maintains a high computational efficiency.The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution. 展开更多
关键词 pseudo arc-length method(PALM) CONSERVATIVE strong discontinuity HIGH-ORDER weighted essentially non-oscillatory(weno)
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Asymptotic solution of a wide moving jam to a class of higher-order viscous traffic flow models 被引量:1
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作者 Chunxiu WU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第5期609-622,共14页
The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and ... The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results. 展开更多
关键词 higher-order traffic flow model wide moving jam boundary-layer method weighted essentially nonoscillatory (weno scheme
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