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Applied Mathematics and Mechanics(English Edition) 2020年第1期41卷 173-192页

作者： Lingyan TANG songhe song Hong ZHANG College of Liberal Arts and Sciences National University of Defense Technology

In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two *** main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case *** test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of *** test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.

关键词： hyperbolic conservation law maximum-principle-preserving(MPP) positivity-preserving(PP) weighted compact nonlinear scheme(WCNS) finite difference scheme

Multi-SymplecticWavelet Collocation Method for Maxwell’s Equations

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Advances in Applied Mathematics and Mechanics 2011年第6期3卷 663-688页

作者： Huajun Zhu songhe song Yaming Chen Department of Mathematics and System Science School of ScienceNational University of Defense TechnologyChangsha 410073China

In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)Maxwell’s *** the multi-symplectic formulation of the equations,wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time *** analysis shows that the proposed method is multi-symplectic,unconditionally stable and energy-preserving under periodic boundary *** numerical dispersion relation is *** with splitting scheme,an explicit splitting symplectic wavelet collocation method is also *** experiments illustrate that the proposed methods are efficient,have high spatial accuracy and can preserve energy conservation laws exactly.

关键词： Multi-symplectic wavelet collocation method Maxwell’s equations symplectic conservation laws

Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation

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Advances in Applied Mathematics and Mechanics 2014年第4期6卷 494-514页

作者： Yaming Chen songhe song Huajun Zhu Department of Mathematics and System Science and State Key Laboratory of High Performance Computing National University of Defense TechnologyChangsha 410073China State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang 621000China

In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)*** on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian *** multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,*** the nonlinear subsystem is solved by a symplectic ***,a composition method is applied to obtain the final schemes for the NLD *** find that the two proposed schemes preserve the total symplecticity and can be solved *** experiments are presented to show the effectiveness of the proposed methods.

关键词： Nonlinear Dirac equation multi-symplectic method splitting method explicit method

Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation

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Advances in Applied Mathematics and Mechanics 2023年第1期15卷 159-181页

作者： Xiaowei Chen Xu Qian songhe song Department of Mathematics National University of Defense TechnologyChangshaHunan 410073China

We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange *** on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal *** analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction,which is independent of the space step ***,the theoretical analysis is verified by several numerical examples.

关键词： Maximum-principle-preserving mass-conserving scheme the conservative AllenCahn equation

Conjugate heat transfer investigations of turbine vane based on transition models

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Chinese Journal of Aeronautics 2013年第4期26卷 890-897页

作者： Zhang Hongjun Zou Zhengping Li Yu Ye Jian song songhe National Key Laboratory of Science and Technology on Aero-Engines School of Energy and Power Engineering Beihang University Science College National University of Defence and Technology

The accurate simulation of boundary layer transition process plays a very important role in the prediction of turbine blade temperature field. Based on the Abu-Ghannam and Shaw （AGS） and c-Re h transition models, a 3D conjugate heat transfer solver is developed, where the fluid domain is discretized by multi-block structured grids, and the solid domain is discretized by unstructured grids. At the unmatched fluid/solid interface, the shape function interpolation method is adopted to ensure the conservation of the interfacial heat flux. Then the shear stress transport （SST） model, SST ＆ AGS model and SST ＆ c-Re h model are used to investigate the flow and heat transfer characteristics of Mark II turbine vane. The results indicate that compared with the full turbulence model （SST model）, the transition models could improve the prediction accuracy of temperature and heat transfer coefficient at the laminar zone near the blade leading edge. Compared with the AGS transition model, the c-Re h model could predict the transition onset location induced by shock/boundary layer interaction more accurately, and the prediction accuracy of temperature field could be greatly improved.

关键词： AGS and c-Re h transition models Conjugate heat transfer Flow and heat transfer char- acteristics Temperature prediction accuracy Transition flow

Novel High-Order Mass-and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrodinger Equation

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Numerical Mathematics(Theory,Methods and Applications) 2023年第4期16卷 993-1012页

作者： Xu Qian Hong Zhang Jingye Yan songhe song Department of Mathematics National University of Defense TechnologyChangsha 410073China College of Mathematics and Physics Wenzhou UniversityWenzhou 325000China

We develop a class of conservative integrators for the regularized logarithmic Schrodinger equation(RLogSE)using the quadratization technique and symplectic Runge-Kutta *** preserve the highly nonlinear energy functional,the regularized equation is first transformed into an equivalent system that admits two quadratic invariants by adopting the invariant energy quadratization *** reformulation is then discretized using the Fourier pseudo-spectral method in the space direction,and integrated in the time direction by a class of diagonally implicit Runge-Kutta schemes that conserve both quadratic invariants to round-off *** comparison purposes,a class of multi-symplectic integrators are developed for RLogSE to conserve the multi-symplectic conservation law and global mass conservation law in the discrete *** experiments illustrate the convergence,efficiency,and conservative properties of the proposed methods.

关键词： Regularized logarithmic Schrödinger equation conservative numerical integrators invariant energy quadratization approach diagonally implicit Runge-Kutta scheme

Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time

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Communications in Computational Physics 2014年第3期15卷 692-711页

作者： Xu Qian Yaming Chen songhe song Department of Mathematics and Systems Science and State Key Laboratory of High Performance ComputingNational University of Defense TechnologyChangsha 410073P.R.China Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA School of Mathematical Sciences Queen Mary University of LondonLondon E14NSUK

In this paper,we propose a wavelet collocation splitting(WCS)method,and a Fourier pseudospectral splitting(FPSS)method as comparison,for solving onedimensional and two-dimensional Schrödinger equations with variable coefficients in quantum *** two methods can preserve the intrinsic properties of original problems as much as *** splitting technique increases the computational ***,the error estimation and some conservative properties are *** is proved to preserve the charge conservation *** global energy and momentum conservation laws can be preserved under several *** experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis.

关键词： Schrödinger equation wavelet collocation method splitting technique conservative property

SOLVING NONLINEAR DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH SINGULAR PERTURBATION VIA BLOCK BOUNDARY VALUE METHODS

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Journal of Computational Mathematics 2023年第4期41卷 643-662页

作者： Xiaoqiang Yan Xu Qian Hong Zhang songhe song Xiujun Cheng College of Liberal Arts and Sciences National University of Defense TechnologyChangsha 410073China State Key Laboratory of High Performance computing National University of Defense TechnologyChangsha 410073China College of Science Zhejiang Sci-Tech UniversityHangzhou 310018China Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China

Block boundary value methods(BBVMs)are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation(DDAESP).It is proved that the extended BBVMs in some suitable conditions are globally stable and can obtain a unique exact solution of the ***,whenever the classic Lipschitz conditions are satisfied,the extended BBVMs are preconsistent and pth order ***,through some numerical examples,the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed.

关键词： Nonlinear delay-diferential-algebraic equations with singular perturbation Block boundary value methods Unique solvability Convergence Global stability

A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations

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Advances in Applied Mathematics and Mechanics 2022年第5期14卷 1181-1200页

作者： Mingyang Cheng Lingyan Tang Yaming Chen songhe song College of Liberal Arts and Sciences National University of Defense TechnologyChangshaHunan 410073China College of Aerospace Science and Engineering National University of Defense TechnologyChangshaHunan 410073China

It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical *** this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced *** scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection *** numerical examples in oneand two-dimensions are also presented to demonstrate the well-balanced property,high order accuracy and good shock capturing capability of the proposed scheme.

关键词： Shallow water equation weighted compact nonlinear scheme well-balanced property shock capturing property

A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes

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Advances in Applied Mathematics and Mechanics 2018年第1期10卷 114-137页

作者： Yunrui Guo Lingyan Tang Hong Zhang songhe song Department of Mathematics and Systems Science and State Key Laboratory of High Performance ComputingNational University of Defense TechnologyChangshaHunan 410073China

We modify the construction of the third order finite volume WENO scheme on triangular meshes and present a simplified WENO(SWENO)*** novelty of the SWENO scheme is the less complexity and lower computational cost when deciding the smoothest stencil through a simple *** LU decomposition with iterative refinement is adopted to implement ill-conditioned interpolation matrices and improves the stability of the SWENOscheme ***,a scaling technique is used to circument the growth of condition numbers as mesh ***,weak oscillations still appear when the SWENO scheme deals with complex low density *** order to guarantee the maximum-principle-preserving(MPP)property,we apply a scaling limiter to the reconstruction polynomial without the loss of accuracy.A novel procedure is designed to prove this property ***,numerical examples for one-and two-dimensional problems are presented to verify the good performance,maximum principle preserving,essentially non-oscillation and high resolution of the proposed scheme.

关键词： Triangular meshes WENO scaling limiter maximum-principle-preserving