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Advances in Aerodynamics 2022年第1期4卷 115-146页

作者： Chuang-Chao Ye Peng-Jun-Yi Zhang Zhen-Hua Wan Rui Yan De-Jun Sun Department of Modern Mechanics University of Science and Technology of ChinaHefeiChina

A high fidelity flow simulation for complex geometries for high Reynolds number(Re)flow is still very challenging,requiring a more powerful HPC system.However,the development of HPC with traditional CPU architecture suffers bottlenecks due to its high power consumption and technical difficulties.Heterogeneous architecture computation is raised to be a promising solution to the challenges of HPC development.GPU accelerating technology has been utilized in low order scheme CFD solvers on the structured grid and high order scheme solvers on unstructured meshes.The high-order finite difference methods on structured grids possess many advantages,e.g.,high efficiency,robustness,and low storage.However,the strong dependence among points for a high-order finite difference scheme still limits its application on the GPU platform.In the present work,we propose a set of hardware-aware technology to optimize data transfer efficiency between CPU and GPU,as well as communication efficiency among GPUs.An in-house multi-block structured CFD solver with high order finite difference methods on curvilinear coordinates is ported onto the GPU platform and obtains satisfying performance with a speedup maximum of around 2000x over a single CPU core.This work provides an efficient solution to apply GPU computing in CFD simulation with specific high order finite difference methods on current GPU heterogeneous computers.The test shows that significant accelerating effects can be achieved for different GPUs.

关键词： Hardware-aware high order Finite difference methods Curvilinear coordinates GPU

high order correlation polarization potential for vibrational excitation scattering of diatomic molecules by low-energy electrons

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Chinese Physics B 2009年第11期18卷 4846-4851页

作者：冯灏孙卫国曾阳阳 School of Physics and Chemistry Xihua University Institute of Atomic and Molecular Physics Sichuan University

This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so that it can better reflect the dependence of correlation and polarization effects on the position coordinate of the scattering electron. It applies the new potential on the vibrational excitation scattering from N2 in an energy range which includes the ^2Ⅱg shape resonance. The good agreement of theoretical resonant peaks with experiments shows that polarization potentials with high order terms are important and should be included in vibrational excitation scattering.

关键词： vibrational excitation scattering correlation-polarization high order resonant

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 grids.The method is easy to implement since it involves one-dimensional operations only,and does not involve surface or volume integrals.Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube.The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy.In this paper,accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions.high order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette flow.The 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.

Z-scan analysis of high-order nonlinear refraction effect induced by using elliptic Gaussian beam

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Chinese Physics B 2010年第6期19卷 541-547页

作者：郭世方田强 Department of Physics Beijing Normal University

The irradiance of an elliptic Gaussian beam that is high enough to excite high-order nonlinear refraction effect is used to calculate the normalized on-axis transmittance function in the z-scan technique by introducing complex beam parameters which make the calculation simpler. The transmittance formula is applied to the first-, first two-, and first three-order nonlinearities. Numerical evaluation shows that the symmetry no longer holds when using an elliptic Gaussian beam instead of a circular Gaussian beam. A distortion is observed in the central part of the curve, which decreases as ellipticity increases. Moreover, the variation of the normalized peak-valley difference decreases as ellipticity decreases.

关键词： z-scan elliptic Gaussian beam complex beam parameter high order

The Properties of Light Pressure Force with high order in Laser Fields

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Chinese Journal of Lasers 2002年第5期11卷 22-27页

作者：陈险峰方建兴朱士群 Department of Physics Suzhou University Suzhou 215006

In this paper, the light pressure force in low and high intensity laser fields is derived. The exact numerical results of forces F n ∥(n=0,1,2,3,4,5,6...) through the matrix continued fraction method are presented. At low intensity field (G=1), the spatially averaged force F 0 ∥ gives a cooling effect at the negative detuning. At high intensity (G=64), the effects of the forces with higher order (n≥2) appear and the contributes of the forces with odd or even order are opposite. It is great different from no high order force at low intensity.

关键词： laser field light pressure force high order odd/even order

WELL-CONDITIONED FRAMES FOR high order FINITE ELEMENT METHODS

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Journal of Computational Mathematics 2021年第3期39卷 333-357页

作者： Kaibo Hu Ragnar Winther School of Mathematics University of Minnesota55455 MinneapolisMNUSA Department of Mathematics University of Oslo0316 OsloNorway

The purpose of this paper is to discuss representations of high order C^(0)finite element spaces on simplicial meshes in any dimension.When computing with high order piecewise polynomials the conditioning of the basis is likely to be important.The main result of this paper is a construction of representations by frames such that the associated L^(2)condition number is bounded independently of the polynomial degree.To our knowledge,such a representation has not been presented earlier.The main tools we will use for the construction is the bubble transform,introduced previously in[1],and properties of Jacobi polynomials on simplexes in higher dimensions.We also include a brief discussion of preconditioned iterative methods for the finite element systems in the setting of representations by frames.

关键词： Finite element method high order Condition number Frame Preconditioner

Efficient Implicit Non-linear LU-SGS Approach for Compressible Flow Computation Using high-order Spectral Difference Method

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Communications in Computational Physics 2009年第2期5卷 760-778页

作者： Yuzhi Sun Z.J.Wang Yen Liu Department of Aerospace Engineering Iowa State UniversityAmesIA 50011USA NASA Ames Research Center Moffett FieldCA 94035USA

An implicit non-linear lower-upper symmetric Gauss-Seidel(LU-SGS)solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids.The non-linear LU-SGS solver is preconditioned by a block element matrix,and the system of equations is then solved with the LU decomposition approach.The large sparse Jacobian matrix is computed numerically,resulting in extremely simple operations for arbitrarily complex residual operators.Several inviscid and viscous test cases were performed to evaluate the performance.The implicit solver has shown speedup of 1 to 2 orders of magnitude over the multi-stage Runge-Kutta time integration scheme.

关键词： high order unstructured grids spectral difference Navier-Stokes implicit

A high-order PAD SCHEME FOR KORTEWEG-DE VRIES EQUATIONS

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Journal of Hydrodynamics 2005年第6期17卷 654-659页

作者： XU Zhen-li LIU Ru-xun Department of Mathematics University of Science and Technology of China Hefei 230026 China

A high-order finite difference Pade scheme also called compact scheme for solving Korteweg-de Vries （KdV） equations, which preserve energy and mass conservations, was developed in this paper. This structure-preserving algorithm has been widely applied in these years for its advantage of maintaining the inherited properties. For spatial discretization, the authors obtained an implicit compact scheme by which spatial derivative terms may be approximated through combining a few knots. By some numerical examples including propagation of single soliton and interaction of two solitons, the scheme is proved to be effective.

关键词： Korteweg-de Vries （KdV） equation compact finite difference scheme solitory waves high order

A Posteriori Stabilized Sixth-order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

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Communications on Applied Mathematics and Computation 2023年第2期5卷 751-775页

作者： Gaspar J.Machado Stéphane Clain Raphaël Loubère Centre of Physics and Department of Mathematics University of MinhoCampus of Azurém4800-058 GuimaraesPortugal CNRS and Institut de Mathématiques de Bordeaux(IMB) Universitéde BordeauxTalenceFrance

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.high accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

关键词： Finite volume MOOD Adaptive stencil Steady-state solution Euler equations high order

INTERVAL OSCILLATION CRITERIA FOR high order NEUTRAL DIFFERENTIAL EQUATIONS WITH CONTINUOUS DEVIATING ARGUMENTS

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Annals of Differential Equations 2006年第3期22卷 411-417页

作者： Yu Xiuping (Dept. of Math, and Physics, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou 075024) Yang Hongyu (Dept. of Mechanic and Engineering, Zhangjiakou Occupation and Technology College, Zhangjiakou 075031)

By introducing two integral operators and using the integral averaging technique, some new oscillation criteria are obtained for a class of high order neutral differential equation with continuous deviating arguments. These results are different from most known ones in the sense that they depend on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line.

关键词： interval oscillation criteria neutral differential equation high order continuous deviating arguments