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Applied Mathematics and Mechanics(English Edition) 2012年第6期33卷 687-700页

作者：黎爱兵张立凤臧增亮张云 Institute of Meteorology PLA University of Science and Technology

The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.

关键词： limited domain stream function velocity potential iteration and adjust-ment convergence

TWO-LEVEL METHOD FOR UNSTEADY NAVIER-STOKES EQUATIONS IN stream function FORM

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Applied Mathematics(A Journal of Chinese Universities) 2005年第1期20卷 105-120页

作者： RenChunfeng MaYichen XuHui CollegeofScience Xi＇anJiaotongUniv.Xi＇an710049China. CollegeofScience Xi＇anJiaotongUniv.Xi＇an710049China.

Two-level finite element approximation to stream function form of unsteady Navier-Stokes equations is *** algorithm involves solving one nonlinear system on a coarse grid and one linear problem on a fine ***,the scaling between these two grid sizes is ***,stability and convergence aspects of a fully discrete scheme are *** last a numrical example is given whose results show that the algorithm proposed in this paper is effcient.

关键词： Navier-Stokes equations two-level method stream function approximation stability convergence.

Approximations to Isentropic Planar Magneto-Hydrodynamics Equations by Relaxed Euler-Type Systems

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 413-440页

作者： Yachun LI Zhaoyang SHANG Chenmu WANG Liang ZHAO School of Mathematical Sciences CMA-ShanghaiMOE-LSC and SHL-MACShanghai Jiao Tong UniversityShanghai 200240China School of Finance Shanghai Lixin University of Accounting and FinanceShanghai 201209China School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of Mathematical Sciences Harbin Engineering UniversityHarbin 150001China Mathematical Modelling&Data Analytics Center Oxford Suzhou Centre for Advanced ResearchSuzhou 215123JiangsuChina

In this paper, the authors consider an approximation to the isentropic planar Magneto-hydrodynamics(MHD for short) equations by a kind of relaxed Euler-type system. The approximation is based on the generalization of the Maxwell law for nonNewtonian fluids together with the Maxwell correction for the Ampe`re law, hence the approximate system becomes a first-order quasilinear symmetrizable hyperbolic systems with partial dissipation. They establish the global-in-time smooth solutions to the approximate Euler-type equations in a small neighbourhood of constant equilibrium states and obtain the global-in-time convergence towards the isentropic planar MHD equations. In addition, they also establish the global-in-time error estimates of the limit based on stream function techniques and energy estimates for error variables.

关键词： Planar MHD equations Relaxation limits Global convergence stream function

Accurate surface normal representation to facilitate gradient coil optimization on curved surface

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Magnetic Resonance Letters 2023年第1期3卷 67-84,I0004页

作者： Hao Ren Hui Pan Feng Jia Jan G.Korvink Zhenyu Liu Changchun Institute of Optics Fine Mechanics and PhysicsChinese Academy of SciencesChangchun130033China School of Optoelectronics University of Chinese Academy of SciencesBeijing101499China Department of Radiology Medical PhysicsMedical Center University of FreiburgFaculty of MedicineUniversity of FreiburgFreiburg79110Germany Institute of Microstructure Technology Karlsruhe Institute of Technology(KIT)Karlsruhe76049Germany

The design methods for gradient coils are mostly based on discrete extrinsic methods(e.g.,the BioteSavart integration calculation),for which the surface normal vector strongly influences any numerical calculation of the discretized *** studies are mostly based on regular or analytical surfaces,which allow normal vectors to be expressed *** certain applications,design methods for extending currentcarrying surfaces from developable or analytic geometries to arbitrary surfaces generated from a scanned point cloud are *** key task is to correctly express the discretized normal vectors to ensure geometrical accuracy of the designed ***,it has been proven that applying a Delaunay triangulation to approximate a smooth surface can result in the discrete elemental normal vectors converging to those of the original ***,this article uses Delaunay triangulation to expand upon previous design methods so that they encompass arbitrary piecewise continuous *** design methods,the stream function and the so-called solid isotropic material with penalization(SIMP)method,are used to design circumvolute and noncircumvolute gradient coils on general surfaces.

关键词： Gradient coils Delaunay triangulation stream function SIMP method

Numerical modeling method on the movement of water flow and suspended solids in two-dimensional sedimentation tanks in the wastewater treatment plant

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Journal of Environmental Sciences 2003年第1期15卷 31-37页

作者： ZENGGuang－ming JIANG－Yi－min 等 DepartmentofEnvironmentalSciencesandEngineeeringofHumanUniversity Changsha410082China

Taking the distributing calculation of velocity and concentration as an example, the paper established a series of governing equations by the vorticity stream function method, and dispersed the equations by the finite differencing method. After figuring out the distribution field of velocity, the paper also calculated the concentration distribution in sedimentation tank by using the two dimensional concentration transport equation. The validity and feasibility of the numerical method was verified through comparing with experimental data. Furthermore, the paper carried out a tentative exploration into the application of numerical simulation of sedimentation tanks.

关键词： sedimentation tank numerical simulation vorticity stream function

Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

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Applied Mathematics and Mechanics(English Edition) 2017年第12期38卷 1697-1708页

作者： V.MISHRA B.R.GUPTA Department of Mathematics Jaypee University of Engineering and TechnologyMadhya Pradesh 473226India

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

关键词： micro-polar fluid permeable sphere Darcy law stream function drag force wall correction factor spherical container

CORRECTION METHODS FOR STEADY INCOMPRESSIBLE FLOWS

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Journal of Computational Mathematics 1999年第4期17卷 419-424页

作者： Jian Li(State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Chinese Academy of Sciences, Beijing 100080, China) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京

Correction methods for the steady semi-periodic motion of incompressible fluid are investigated. The idea is similar to the influence matrix to solve the lack of vorticity boundary conditions. For any given boundary condition of the vorticity, the coupled vorticity-stream function formulation is solved. Then solve the governing equations with the correction boundary conditions to improve the solution. These equations are numerically solved by Fourier series truncation and finite difference method. The two numerical techniques are employed to treat the non-linear terms. The first method for small Reynolds number R equals 0-50 has the same results as that in M. Anwar and S.C.R. Dennis' report. The second one for R greater than 50 obtains the reliable results. (Author abstract) 4 Refs.

关键词： incompressible flow vorticity stream function numerical solution

Hodograph method of flow on two-dimensional manifold

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Applied Mathematics and Mechanics(English Edition) 2010年第3期31卷 363-376页

作者：李开泰史峰 School of Science Xi'an Jiaotong University

For some special flows, especially the potential flow in a plane, using the hodograph method has obvious advantages. Realistic flows have a stream surface, namely, a two-dimensional manifold, on which the velocity vector of the flow lies on its tangent space. By introducing a stream function and a potential function, we establish the hodo- graph method for potential flows on a surface using the tensor analysis. For the derived hodograph equation, we obtain a characteristic equation and its characteristic roots, from which we can classify the type of the second-order hodograph equation. Moreover, we give some examples for special surfaces.

关键词： hodograph method potential flow stream surface stream function potential function

The Spectral Method for the Flow between Two Concentric Rotating Spheres, Part I:The Full Discrete Nonlinear Legendre-Galerkin Method

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Communications in Nonlinear Science and Numerical Simulation 1998年第4期3卷 211-214页

作者： Weibing FENG and Kaitai LI (Institute of Appl. Math. & Mech., Shanghai Uni., Shanghai 200072, China)(Science College, Xi’an Jiaotong University, Xi’an 710049, China)E--mail: glliu@*** Institute of Appl. Math. and Mech. Shanghai Univ. Shanghai 200072 China Science College Xi'an Jiaotong University Xi'an 710049 China

The nonlinear Galerkin methods are numerical schemes for evolutionary partial differential equations based on the theory of inertial manifolds and approximate inertial manifolds. In this paper, we consider the flow between two concentric rotating spheres, and combine the Legendre-Galerkin spectral methods in Part I together with the nonlinear Galerkin method, then construct the full discrete nonlinear Legendle-Galerkin spectral scheme, and derive the stability conditions and its error estimate.

关键词： Navier-Stokes equations nonlinear Galerkin method stream function

THREE-DIMENSIONAL ANALYSIS OF THE FLOW IN THE CYCLONES

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Applied Mathematics and Mechanics(English Edition) 1995年第6期16卷 557-564页

作者：奚致中 Anhui Institute of Finance and Trade Bengbu Auhui P. R. China

This paper gives the detailed mathematical expression of the flow in the spherical coordinates system. Applying the law of conservation of mass, movement theorem of steady flow, and applying the mathematical method of stream function with consideration of the axis symmetry, the three components of velocity quantum of the flow are deduced in detail. Here the overall analysis of the flow is presented in the view of the concept of whole, and the paper gives the necessary corrections of some results of Ref.[1]

关键词： three-dimensional flow stream function steady flow incompressible fluid