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A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE advection-diffusion equationS

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Journal of Computational Mathematics 2002年第1期20卷 57-64页

作者： Huo-yuan Duan (Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China) Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the development of a stabilized finite element method for solving the advection-diffusion equations with a zero Dirichlet boundary condition. Problem formulation; Error analysis.

关键词： advection-diffusion equation stabilized finite element method

A Family of Characteristic Discontinuous Galerkin Methods for Transient advection-diffusion equations and Their Optimal-Order L2 Error Estimates

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Communications in Computational Physics 2009年第6期6卷 203-230页

作者： Kaixin Wang Hong Wang Mohamed Al-Lawatia Hongxing Rui School of Mathematics and System Sciences Shandong UniversityJinanShandong 250100China Department of Mathematics University of South CarolinaColumbiaSouth Carolina 29208USA Department of Mathematics and Statistics Sultan Qaboos UniversityP.O.Box 36Al-Khod 123Sultanate of Oman

We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations,including the characteristic NIPG,OBB,IIPG,and SIPG *** derived schemes possess combined advantages of EulerianLagrangian methods and discontinuous Galerkin *** optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG,IIPG,and SIPG *** experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG,OBB,IIPG,and SIPG schemes in the context of advection-diffusion equations.

关键词： advection-diffusion equation characteristic method discontinuous Galerkin method numerical analysis optimal-order L2 error estimate superconvergence estimate

UNIFORM OPTIMAL-ORDER ESTIMATES FOR FINITE ELEMENT METHODS FOR advection-diffusion equationS

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Journal of Systems Science & Complexity 2009年第4期22卷 555-559页

作者： Qun LIN Hong WANG Shuhua ZHANG Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of SciencesBeijing 100190 China. Department of Mathematics University of South Carolina Columbia South Carolina 29208 USA. Research Center for Mathematics and Economics Tianjin University of Finance and Economics Tianjin300222 China.

This article summarizes our recent work on uniform error estimates for various finite elementmethods for time-dependent advection-diffusion equations.

关键词： advection-diffusion equation bilinear finite element method linear triangular elementmethod nonconforming finite element method.

Solution of Nonlinear advection-diffusion equations via Linear Fractional Map Type Nonlinear QCA

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Journal of Quantum Information Science 2016年第4期6卷 263-295页

作者： Shinji Hamada Hideo Sekino Toyohashi University of Technology Toyohashi Japan Stony Brook University New York USA Tokyo Institute of Technology Tokyo Japan

Linear fractional map type (LFMT) nonlinear QCA (NLQCA), one of the simplest reversible NLQCA is studied analytically as well as numerically. Linear advection equation or Time Dependent Schrödinger equation (TDSE) is obtained from the continuum limit of linear QCA. Similarly it is found that some nonlinear advection-diffusion equations including inviscid Burgers equation and porous-medium equation are obtained from LFMT NLQCA.

关键词： Nonlinear Quantum Cellular Automaton QCA Quantum Walk Linear Fractional Map advection-diffusion equation Burgers equation Porous-Medium equation Soliton

Application of advection-diffusion Routing Model to Flood Wave Propagation： A Case Study on Big Piney River, Missouri USA

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Journal of Earth Science 2016年第1期27卷 9-14页

作者： Yang Yang Theodore A. Endreny David J. Nowak USDA Forest Service Northern Research Station & the Davey Institute Syracuse NY 13210 USA Environmental Resource Engineering SUNY ESF Syracuse NY 132 10 USA USDA Forest Service Northern Research Station Syracuse NY 13210 USA

Flood wave propagation modeling is of critical importance to advancing water resources management and protecting human life and property. In this study, we investigated how the advection-diffusion routing model performed in flood wave propagation on a 16 km long downstream section of the Big Piney River, MO. Model performance was based on gaging station data at the upstream and downstream cross sections. We demonstrated with advection-diffusion theory that for small differences in watershed drainage area between the two river cross sections, inflow along the reach mainly contributes to the downstream hydrograph＇s rising limb and not to the falling limb. The downstream hydrograph＇s falling limb is primarily determined by the propagated flood wave originating at the upstream cross section. This research suggests the parameter for the advectiondiffusion routing model can be calibrated by fitting the hydrograph falling limb. Application of the advection diffusion model to the flood wave of January 29, 2013 supports our theoretical finding that the propagated flood wave determines the downstream cross section falling limb, and the model has good performance in our test examples.

关键词： advection-diffusion equation hydrograph flood wave propagation recession limb.

Lattice Boltzmann Simulation of Free-Surface Temperature Dispersion in Shallow Water Flows

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Advances in Applied Mathematics and Mechanics 2009年第3期1卷 415-437页

作者： Mohammed Seaid Guido Thommes School of Engineering University of DurhamSouth RoadDurham DH13LEUK Fraunhofer-Institut fur Techno-und Wirtschaftsmathematik 67663 KaiserslauternGermany

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water *** governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including bed frictions,eddy viscosity,wind shear stresses and Coriolis *** thermal effects are incorporated in the momentum equation by using a Boussinesq *** dispersion of free-surface temperature is modelled by an advection-diffusion *** distribution functions are used in the lattice Boltzmann method to recover the flow and temperature variables using the same lattice *** upwind discretization procedures nor Riemann problem solvers are needed in discretizing the shallow water *** addition,the source terms are straightforwardly included in the model without relying on well-balanced techniques to treat flux gradients and source *** validate the model for a class of problems with known analytical solutions and we also present numerical results for sea-surface temperature distribution in the Strait of Gibraltar.

关键词： Shallow water flows free-surface temperature lattice Boltzmann method advection-diffusion equation strait of Gibraltar

Application of the finite analytic numerical method to a flowdependent variational data assimilation

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Acta Oceanologica Sinica 2024年第3期43卷 30-39页

作者： Yan Hu Wei Li Xuefeng Zhang Guimei Liu Liang Zhang Tianjin Key Laboratory for Marine Environmental Research and Service School of Marine Science and TechnologyTianjin UniversityTianjin 300072China School of Marine Science and Technology Tianjin UniversityTianjin 300072China National Marine Environmental Forecasting Center Ministry of Natural ResourcesBeijing 100081China

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion *** of the directionality of the advection term,the discrete method needs to be chosen very *** finite analytic method is an alternative scheme to solve the advection-diffusion *** a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto *** demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic *** more widely used upwind difference method is used as a control *** result indicates that the finite analytic method has higher accuracy than the upwind difference *** the two-dimensional case,the finite analytic method still has a better *** the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference ***,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

关键词： finite analytic method advection-diffusion equation data assimilation flow-dependent

A Well-Balanced and Non-Negative Numerical Scheme for Solving the Integrated Shallow Water and Solute Transport equations

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Communications in Computational Physics 2010年第5期7卷 1049-1075页

作者： Qiuhua Liang School of Civil Engineering and Geosciences Newcastle UniversityNewcastle upon TyneNE17RUEnglandUK

Based on the recent development in shallow flow modelling, this paperpresents a finite volume Godunov-type model for solving a 4×4 hyperbolic matrixsystem of conservation laws that comprise the shallow water and depth-averaged solute transport equations. The adopted governing equations are derived to preserveexactly the solution of lake at rest so that no special numerical technique is necessaryin order to construct a well-balanced scheme. The HLLC approximate Riemann solveris used to evaluate the interface fluxes. Second-order accuracy is achieved using theMUSCL slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is validated against several benchmark tests and the resultsare in excellent agreement with analytical solutions or other published numerical predictions.

关键词： Solute transport shallow water equations advection-diffusion equation wellbalanced scheme wetting and drying source terms Riemann solver

An Analytical Formulation for Pollutant Dispersion Simulation in the Atmospheric Boundary Layer

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Journal of Environmental Protection 2013年第8期4卷 57-64页

作者： Glenio A.Goncalves Regis S.de Quadros Daniela Buske Federal University of Pelotas(UFPel) Department of Mathematics and Statistics(IFM/DME)PelotasBrazil

In this work we present the solution of the two-dimensional advection-diffusion equation by the GILTT method. The GILTT approach uses, in the series expansion, eigenfunctions given in terms of cosine functions. Here, a different expansion for the solution of the advection-diffusion equation will be explored. In other words, a Sturm-Liouville problem carrying more information of the original problem is considered, given by Bessel functions. Numerical simulations and comparisons with experimental data are presented.

关键词： Analytical Solution advection-diffusion equation Air Pollution Modeling Integral Transform Bessel Functions