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| 1 | Conjugate heat transfer investigations of turbine vane based on transition models显示文摘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. | Zhang Hongjun Zou Zhengping Li Yu Ye Jian Song Songhe | 2013 | Chinese Journal of Aeronautics2013，26，4： | 5 |
| 2 | High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws显示文摘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 dimensions.The 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 discussion.Smooth 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 accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes. | Lingyan TANG Songhe SONG Hong ZHANG | 2020 | Applied Mathematics and Mechanics(English Edition)2020，41，1： | 3 |
| 3 | Effect of sericin on diabetic hippocampal growth hormone/insulin-like growth factor 1 axis显示文摘Previous studies have shown that sericin extracted from silk cocoon significantly reduces blood glucose levels and protects the nervous system against diabetes mellitus. In this study, a rat type 2 diabetes mellitus model was established by intraperitoneal injection of 25 mg/kg streptozotocin for 3 successive days, following which the rats were treated with sericin for 35 days. After treatment, the blood glucose levels of the diabetic rats decreased significantly, the growth hormone level in serum and its expression in the hippocampus decreased significantly, while the insulin-like growth factor-1 level in serum and insulin-like growth factor-1 and growth hormone receptor expression in the hippocampus increased significantly. The experimental findings indicate that sericin improves disorders of the growth hormone/insulin-like growth factor 1 axis to alleviate hippocampal damage in diabetic rats. | Zhihong Chen Songhe Yang Yaqiang He Chengjun Song Yongping Liu | 2013 | Neural Regeneration Research2013，8，19： | 2 |
| 4 | A multiresolution finite volume scheme for two-dimensional hyperbol- ic conservation laws显示文摘 | Tang Lingyan Song Songhe | 2008 | Journal of Computational and Applied Mathematics2008，214，： | 1 |
| 5 | A multiresolution finite volume scheme for two-dimensional hyperbolic conservation laws 显示文摘 | Tang Lingyan Song Songhe | 2008 | J Comput Appl Math2008，214，： | 1 |
| 6 | A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes显示文摘We modify the construction of the third order finite volume WENO scheme on triangular meshes and present a simplified WENO(SWENO)scheme.The novelty of the SWENO scheme is the less complexity and lower computational cost when deciding the smoothest stencil through a simple mechanism.The LU decomposition with iterative refinement is adopted to implement ill-conditioned interpolation matrices and improves the stability of the SWENOscheme efficiently.Besides,a scaling technique is used to circument the growth of condition numbers as mesh refined.However,weak oscillations still appear when the SWENO scheme deals with complex low density equations.In 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 theoretically.Finally,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. | Yunrui Guo Lingyan Tang Hong Zhang Songhe Song | 2018 | Advances in Applied Mathematics and Mechanics2018，10，1： | 1 |
| 7 | Novel Conservative Methods for Schrödinger Equations with Variable Coefficients over Long Time显示文摘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 mechanics.The two methods can preserve the intrinsic properties of original problems as much as possible.The splitting technique increases the computational efficiency.Meanwhile,the error estimation and some conservative properties are investigated.It is proved to preserve the charge conservation exactly.The global energy and momentum conservation laws can be preserved under several conditions.Numerical experiments are conducted during long time computations to show the performances of the proposed methods and verify the theoretical analysis. | Xu Qian Yaming Chen Songhe Song | 2014 | Communications in Computational Physics2014，15，3： | 0 |
| 8 | Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schr odinger System显示文摘This paper introduces two novel conformal structure-preserving algorithms for solving the coupled damped nonlinear Schr¨odinger(CDNLS)system,which are based on the conformal multi-symplectic Hamiltonian formulation and its conformal conservation laws.The proposed algorithms can preserve corresponding conformal multi-symplectic conservation lawand conformalmomentum conservation lawin any local time-space region,respectively.Moreover,it is further shown that the algorithms admit the conformal charge conservation law,and exactly preserve the dissipation rate of charge under appropriate boundary conditions.Numerical experiments are presented to demonstrate the conformal properties and effectiveness of the proposed algorithms during long-time numerical simulations and validate the analysis. | Hao Fu Weien Zhou Xu Qian Songhe Song | 2017 | Advances in Applied Mathematics and Mechanics2017，9，6： | 0 |
| 9 | Multi-SymplecticWavelet Collocation Method for Maxwell’s Equations显示文摘In this paper,we develop a multi-symplectic wavelet collocation method for three-dimensional(3-D)Maxwell’s equations.For 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 integration.Theoretical analysis shows that the proposed method is multi-symplectic,unconditionally stable and energy-preserving under periodic boundary conditions.The numerical dispersion relation is investigated.Combined with splitting scheme,an explicit splitting symplectic wavelet collocation method is also constructed.Numerical experiments illustrate that the proposed methods are efficient,have high spatial accuracy and can preserve energy conservation laws exactly. | Huajun Zhu Songhe Song Yaming Chen | 2011 | Advances in Applied Mathematics and Mechanics2011，3，6： | 0 |
| 10 | A Well-Balanced Weighted Compact Nonlinear Scheme for Pre-Balanced Shallow Water Equations显示文摘It is well known that developing well-balanced schemes for the balance laws is useful for reducing numerical errors.In this paper,a well-balanced weighted compact nonlinear scheme(WCNS)is proposed for shallow water equations in prebalanced forms.The scheme is proved to be well-balanced provided that the source term is treated appropriately as the advection term.Some 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. | Mingyang Cheng Lingyan Tang Yaming Chen Songhe Song | 2022 | Advances in Applied Mathematics and Mechanics2022，14，5： | 0 |
| 11 | SOLVING NONLINEAR DELAY-DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH SINGULAR PERTURBATION VIA BLOCK BOUNDARY VALUE METHODS显示文摘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 DDAESP.Besides,whenever the classic Lipschitz conditions are satisfied,the extended BBVMs are preconsistent and pth order consistent.Moreover,through some numerical examples,the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed. | Xiaoqiang Yan Xu Qian Hong Zhang Songhe Song Xiujun Cheng | 2023 | Journal of Computational Mathematics2023，41，4： | 0 |
| 12 | Robust and Quality Boundary Constrained Tetrahedral Mesh Generation显示文摘A novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique(AFT)and conforming Delaunay triangulation.Given a triangulated surface mesh,AFT is firstly applied to mesh several layers of elements adjacent to the boundary.The rest of the domain is then meshed by the conforming Delaunay triangulation.The non-conformal interface between two parts of meshes are adjusted.Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality.Robustness and quality of the proposed method is shown.Convergence proof of each stage as well as the whole algorithm is provided.Various numerical examples are included as well as the quality of the meshes. | Songhe Song Min Wan Shengxi Wang Desheng Wang Zhengping Zou | 2013 | Communications in Computational Physics2013，14，10： | 0 |
| 13 | Explicit Multi-Symplectic Splitting Methods for the Nonlinear Dirac Equation显示文摘In this paper,we propose two new explicit multi-symplectic splitting methods for the nonlinear Dirac(NLD)equation.Based on its multi-symplectic formulation,the NLD equation is split into one linear multi-symplectic system and one nonlinear infinite Hamiltonian system.Then multi-symplectic Fourier pseudospectral method and multi-symplectic Preissmann scheme are employed to discretize the linear subproblem,respectively.And the nonlinear subsystem is solved by a symplectic scheme.Finally,a composition method is applied to obtain the final schemes for the NLD equation.We find that the two proposed schemes preserve the total symplecticity and can be solved explicitly.Numerical experiments are presented to show the effectiveness of the proposed methods. | Yaming Chen Songhe Song Huajun Zhu | 2014 | Advances in Applied Mathematics and Mechanics2014，6，4： | 0 |
| 14 | Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation显示文摘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 multiplier.Based on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal direction.Theoretical 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 size.Finally,the theoretical analysis is verified by several numerical examples. | Xiaowei Chen Xu Qian Songhe Song | 2023 | Advances in Applied Mathematics and Mechanics2023，15，1： | 0 |
| 15 | A Splitting Method for the Degasperis-Procesi Equation Using an Optimized WENO Scheme and the Fourier Pseudospectral Method显示文摘The Degasperis-Procesi(DP)equation is split into a system of a hyperbolic equation and an elliptic equation.For the hyperbolic equation,we use an optimized finite difference weighted essentially non-oscillatory(OWENO)scheme.New smoothness measurement is presented to approximate the typical shockpeakon structure in the solution to the DP equation,which evidently reduces the dissipation arising from discontinuities simultaneously removing nonphysical oscillations.For the elliptic equation,the Fourier pseudospectral method(FPM)is employed to discretize the high order derivative.Due to the combination of the WENO reconstruction and FPM,the splitting method shows an excellent performance in capturing the formation and propagation of shockpeakon solutions.The numerical simulations for different solutions of the DP equation are conducted to illustrate the high accuracy and capability of the method. | Yunrui Guo Wenjing Yang Hong Zhang Ji Wang Songhe Song | 2019 | Advances in Applied Mathematics and Mechanics2019，11，1： | 0 |
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