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A Parameter–Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids

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Advances in Applied Mathematics and Mechanics 2009年第4期1卷 451-480页

作者： Michael Yang z.j.wang Department of Aerospace Engineering and CFD Center Iowa State UniversityAmesIA 50011USA

A parameter-free limiting technique is developed for high-order unstructured-grid methods to capture discontinuities when solving hyperbolic conservation *** technique is based on a“troubled-cell”approach,in which cells requiring limiting are first marked,and then a limiter is applied to these marked cells.A parameter-free accuracy-preserving TVD marker based on the cell-averaged solutions and solution derivatives in a local stencil is compared to several other markers in the literature in identifying“troubled cells”.This marker is shown to be reliable and efficient to consistently mark the *** a compact highorder hierarchical moment limiter is developed for arbitrary unstructured *** limiter preserves a degree p polynomial on an arbitrary *** a result,the solution accuracy near smooth local extrema is *** results for the high-order spectral difference methods are provided to illustrate the accuracy,effectiveness,and robustness of the present limiting technique.

关键词： Limiter shock-capturing high-order unstructured grids

A Mathematical Analysis of Scale Similarity

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Communications in Computational Physics 2017年第1期21卷 149-161页

作者： z.j.wang Yanan Li Department of Aerospace Engineering University of Kansas2120 Learned HallLawrenceKS 66045USA

Scale similarity is found in many natural phenomena in the universe,from fluid dynamics to *** large eddy simulations of turbulent flows,some sub-grid scale(SGS)models are based on scale *** earliest scale similarity SGS model was developed by Bardina et al.,which produced SGS stresses with good correlation to the true *** the present study,we perform a mathematical analysis of scale *** analysis has revealed that the ratio of the resolved stress to the SGS stress is g2,where g is the ratio of the second filter width to the first filter width,under the assumption of small filter *** implications of this analysis are discussed in the context of large eddy simulation.

关键词： Scale similarity large eddy simulation sub-grid scale models

Benchmark for scale-resolving simulation with curved walls: the Taylor Couette flow

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Advances in Aerodynamics 2021年第1期3卷 281-298页

作者： z.j.wang E.jourdan Department of Aerospace Engineering University of KansasLawrenceKS 66045USA

Flow between rotating concentric cylinders,or the Taylor Couette flow,has been studied extensively because of its rich physics,ranging from axisymmetric steady laminar flow,to fully developed turbulent *** the present study,we advocate the use of this problem as a benchmark case for scale-resolving simulation,such as large eddy simulation(LES)and direct numerical simulation(DNS).The problem is attractive because of its simple geometry,simple boundary conditions,and complex physics involving wall-shear induced and centrifugal *** the wellknown fully developed channel flow,this problem has a curved wall boundary,and it is unnecessary to add a source term to the governing equations to sustain the fully developed turbulent flow.A p-refinement study for Re=4000 is performed first to establish DNS data,including the time history of enstrophy,which can be used as an accuracy and resolution indicator to evaluate numerical methods,and is orders of magnitude faster than using the mean flow quantities and Reynolds stresses to evaluate solution ***,an hp-refinement study is performed to establish the relative accuracy and efficiency of high-order schemes of various accuracy.

关键词： Large eddy simulation Direct numerical simulation High-order methods Navier-Stokes Taylor Couette flow

The η-Pairing Superconductivity in Spin-Density Wave Background

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Chinese Physics Letters 1993年第10期10卷 616-619页

作者： X.M.Qiu z.j.wang Southwestern Institute of Physics P.O.Box 432Chengdu 610041

In this letter,we propose a modified attractive Hubbard model at half filling that can exhibit sup er con ductivity through η-pairing *** in spin-density wave representation and derive a concise relationship between the energy disparity and the single-particle energy *** relationship,in the two limits of U,clearly shows that the system does not display sup er con ductivity for very low doping concen・*** *** s up ere on ductivity when the doping concentration exceeds a certain critical *** conclusion is in quajitative agreement with the familiar experiments on higli-T_(c) supcrconductivity.

关键词： spectrum value doping

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

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Communications in Computational Physics 2009年第10期6卷 978-996页

作者： Takanori Haga Keisuke Sawada z.j.wang Department of Aerospace Engineering Tohoku UniversitySendai 980-8579Japan Department of Aerospace Engineering Iowa State UniversityAmesIA 50011USA

An efficient implicit lower-upper symmetric Gauss-Seidel(LU-SGS)solution approach has been applied to a high order spectral volume(SV)method for unstructured tetrahedral *** LU-SGS solver is preconditioned by the block element matrix,and the system of equations is then solved with a LU *** compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order *** developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems.A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.

关键词： High-order unstructured grid spectral volume implicit method

High-Order Multidomain Spectral Difference Method for the Navier-Stokes Equations on Unstructured Hexahedral Grids

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Communications in Computational Physics 2007年第2期2卷 310-333页

作者： Yuzhi Sun z.j.wang Yen Liu Department of Aerospace Engineering Iowa State University2271 Howe HallAmesIA 50011USA NASA Ames Research Center Mail Stop T27B-1Moffett FieldCA 94035USA

A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral *** method is easy to implement since it involves one-dimensional operations only,and does not involve surface or volume *** reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit *** concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order *** this paper,accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical *** order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette *** capability of the method for both inviscid and viscous flow problems with curved boundaries is also demonstrated.

关键词： High order unstructured grids spectral difference Navier-Stokes.

On the mesh resolution of industrial LES based on the DNS of flow over the T106C turbine

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Advances in Aerodynamics 2019年第1期1卷 408-425页

作者： Mohammad Alhawwary z.j.wang Department of Aerospace Engineering University of KansasLawrenceKS66045US

A high-order Navier-Stokes solver based on the flux reconstruction(FR)or the correction procedure via reconstruction(CPR)formulation is employed to perform a direct numerical simulation(DNS)and large eddy simulations(LES)of a well-known benchmark problem–transitional flow over the low-pressure T106C turbine ***-refinement studies are carried out to assess the resolution requirement.A 4th order(p3)simulation on the fine mesh is performed with a DNS resolution to establish a"converged"solution,including the mean pressure and skin-friction distributions,and the power spectral density in the *** LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the *** particular,we study the error in the transition location,the mean skin-friction distribution,and the mean lift and drag *** h-and p-refinement studies provide a much-needed guideline in h-and p-resolutions to achieve a certain level of accuracy for industrial LES applications.

关键词： Direct numerical simulations Large eddy simulations Transitional flows High-order FR/CPR T106C Skin-friction

Large Eddy Simulation of Flow over a Cylinder Using High-Order Spectral Difference Method

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Advances in Applied Mathematics and Mechanics 2010年第4期2卷 451-466页

作者： Abrar H.Mohammad z.j.wang Chunlei Liang Department of Aerospace Engineering Iowa State UniversityAmesIA 50011U.S.A Department of Aeronautics and Astronautics Stanford UniversityStanfordCA 94305U.S.A

Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD=2580 has been studied with a high-order unstructured spectral difference *** and polynomial refinement studies were carried out to assess numerical *** mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental *** numerical results are in excellent agreement with the experimental data for both the mean velocity and Reynolds stresses using the high-order SD *** wake characteristics such as the recirculation bubble length,vortex formation length and maximum intensity of the velocity fluctuations have also been predicted *** numerical simulations demonstrated the potential of the high-order SD method in accurate large eddy simulation of physically complex problems.

关键词： LES spectral difference circular cylinder coherent structures vortex shedding

Differential Formulation of Discontinuous Galerkin and Related Methods for the Navier-Stokes Equations

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Communications in Computational Physics 2013年第4期13卷 1013-1044页

作者： Haiyang Gao z.j.wang H.T.Huynh Department of Aerospace Engineering and CFD Center Iowa State University2271 Howe Hall AmesIA 50011USA NASA Glenn Research Center MS 5-11ClevelandOH 44135USA

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 *** addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral *** discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous *** 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 *** stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried ***,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.

关键词： Discontinuous Galerkin lifting collocation penalty flux reconstruction Navier-Stokes equations correction procedure via reconstruction unstructured hybrid grids