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Transport mechanisms of contaminants released from fine sediment in rivers

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Acta Mechanica Sinica 2015年第6期31卷 791-798页

作者： Pengda Cheng Hongwei Zhu Baochang Zhong Daozeng Wang institute of mechanics Chinese Academy of Sciences Shanghai institute of applied mathematics and mechanics Shanghai University

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment （D90 = 0.06 mm）, non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of mole- cular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear st

关键词： Cohesive Diffusion Seepage boundarylayer. Adsorption/desorption Coupling

Hybrid natural element method for large deformation elastoplasticity problems

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Chinese Physics B 2015年第3期24卷 31-39页

作者：马永其周延凯 Shanghai institute of applied mathematics and mechanics Shanghai University Department of mechanics Shanghai University

We present the hybrid natural element method（HNEM） for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger–Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation *** with the natural element method（NEM）, the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.

关键词： hybrid natural element method large deformation elastoplasticity Hellinger–Reissner variational principle meshless method

UPWIND LOCAL DIFFERENTIAL QUADRATURE METHOD FOR SOLVING COUPLED VISCOUS FLOW AND HEAT TRANSFER EQUATIONS

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applied mathematics and mechanics(English Edition) 2004年第10期25卷 1130-1138页

作者： A.S.J.Al-Saif 朱正佑 Shanghai institute of applied mathematics and mechanics Shanghai University

The differential quadrature method (DQM) has been applied successfully to solve numerically many problems in the fluid mechanics. But it is only limited to the flow problems in regular regions. At the same time, here is no upwind mechanism to deal with the convective property of the fluid flow in traditional DQ method. A local differential quadrature method owning upwind mechanism (ULDQM) was given to solve the coupled problem of incompressible viscous flow and heat transfer in an irregular region. For the problem of flow past a contraction channel whose boundary does not parallel to coordinate direction, the satisfactory numerical solutions were obtained by using ULDQM with a few grid points. The numerical results show that the ULDQM possesses advantages including well convergence, less computational workload and storage as compared with the low-order finite difference method.

关键词： upwind locall DQM Navier-Stokes equation heat equation

Non-Linear Synthesis problems for Plane Radiating Systems According to the Prescribed Power Directivity Pattern

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Open Journal of Antennas and Propagation 2013年第2期1卷 23-34页

作者： Mykhaylo Andriychuk Petro Savenko Myroslava Tkach pidstryhach institute for applied problems in mechanics and mathematics NASU Lviv Ukraine

A variational formulation of the synthesis problem for plane radiating systems according to the prescribed power directivity pattern (DP) is considered. The function representing the mean-square deviation of the prescribed and synthesized power DPs and containing the additional term with squared norm of the current or field in the antenna aperture is considered as the criterion of optimization. Freedom to choose the phase DP is used to improve the proximity of the prescribed and synthesized DPs. In such formulation, the classes of non-linear problems, for which the non-uniqueness of solutions, their branching and bifurcation are characteristic, arise. The properties of solutions depend on the electric size of radiating system and prescribed power DP. From a practical point of view, the existence of different solutions creating the same or similar DPs, gives the opportunity to choose the solution that has a simpler implementation. The synthesis problems for plane radiating systems and plane arrays are considered.

关键词： Power Radiation Pattern Synthesis Problem Non-Linear Equation Bifurcation of Solutions Numerical Modeling

Combining the complex variable reproducing kernel particle method and the finite element method for solving transient heat conduction problems

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Chinese Physics B 2013年第5期22卷 67-74页

作者：陈丽马和平程玉民 Department of mathematics Shanghai University Department of Engineering mechanics Chang'an University Shanghai institute of applied mathematics and mechanics Shanghai University

In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.

关键词： complex variable reproducing kernel particle method finite element method combined method,transient heat conduction

CHEBYSHEV APPROXIMATION OF THE SECOND KIND OF MODIFIED BESSEL FUNCTION OF ORDER ZERO

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applied mathematics and mechanics(English Edition) 2004年第5期25卷 483-487页

作者：张璟周哲玮 Shanghai institute of applied mathematics and mechanics Shanghai University

The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by ***'s rational Chebyshe... 详细信息

关键词： second kind of modified Bessel function of order zero exponential transformation rational Chebyshev basis

Some theoretical problems on variational data assimilation

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applied mathematics and mechanics(English Edition) 2007年第5期28卷 651-663页

作者：滕加俊张瑰黄思训 Shanghai institute of applied mathematics and mechanics Shanghai University Department of mathematics and Physics Institute of Science

Theoretical aspects of variational data assimilation （VDA） for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the vahdity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.

关键词： variational data assimilation (VDA) regularization method estimates of convergence rate

A Meshless Collocation Method with Barycentric Lagrange Interpolation for Solving the Helmholtz Equation

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Computer Modeling in Engineering & Sciences 2021年第1期126卷 25-54页

作者： Miaomiao Yang Wentao Ma Yongbin Ge institute of applied mathematics and mechanics Ningxia UniversityYinchuan750021China

In this paper,Chebyshev interpolation nodes and barycentric Lagrange interpolation basis function are used to deduce the scheme for solving the Helmholtz *** of all,the interpolation basis function is applied to treat the spatial variables and their partial derivatives,and the collocation method for solving the second order differential equations is ***,the differential matrix is used to simplify the given differential equations on a given test ***,based on three kinds of test nodes,numerical experiments show that the present scheme can not only calculate the high wave numbers problems,but also calculate the variable wave numbers *** addition,the algorithm has the advantages of high calculation accuracy,good numerical stability and less time consuming.

关键词： Helmholtz equation Chebyshev interpolation nodes Barycentric Lagrange interpolation meshless collocation method high wave number variable wave number

A new complex variable meshless method for transient heat conduction problems

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Chinese Physics B 2012年第12期21卷 42-50页

作者：王健菲程玉民 Shanghai institute of applied mathematics and mechanics Shanghai University Shanghai Key Laboratory of mechanics in Energy Engineering Shanghai University

In this paper, based on the improved complex variable moving least-square （ICVMLS） approximation, a new complex variable meshless method （CVMM） for two-dimensional （2D） transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

关键词： meshless method improved complex variable moving least-square approximation com-plex variable meshless method transient heat conduction problem