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FULL DISCRETE NONLINEAR GALERKIN method FOR THE NAVIER-STOKES EQUATIONS　

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Applied Mathematics(A Journal of Chinese Universities) 1994年第1期9卷 11-30页

作者： LIKAITAI HEYINNIAN XIANGYIMIN InstituteofComputationalandAppliedMathematics Xi＇anJiaotongUniversityXi＇an710049 InstituteofComputationalandAppliedMathematics Xi＇anJiaotongUniversityXi＇an710049

This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the erro... 详细信息

关键词： Full Discrete Nonlinear Galerkin method fractional step method Approximate Inertial Manifold Navier-Stokes Equations.AMS Subject Classification.65N30 65M60.

Fast flow simulation study of pulsating ventilation performance on air contaminant removal

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Building Simulation 2024年第8期17卷 1309-1322页

作者： Pengzhi Zhou Haidong Wang Yuwei Dai Chen Huang School of Environment and Architecture University of Shanghai for Science and Technology516 Jungong RoadShanghai200093China

Fast flow simulation is imperative in the design of pulsating ventilation,which is potentially efficient in indoor air contaminant *** execution of the conventional CFD method requires considerable amount of computational *** this study,five different numerical schemes were proposed based on fast fluid dynamics(FFD)and fractional step(FS)methods,and were evaluated to achieve quick simulation of airflow/contaminant *** of these numerical schemes was identified with the best overall computing efficiency for investigating the performance of pulsating *** this numerical scheme at hand,the air contaminant removal effectiveness of different ventilation types was *** kinds of pulsating ventilation and one kind of steady ventilation were tested upon a benchmark isothermal mixing *** effect of adjusting supply velocity parameters on the ventilation performance was also ***_(2)concentration,airflow pattern,and vortex structure of different ventilation types were illustrated and *** results reveal that the FS method is more suitable for transient simulation of wall-bounded indoor airflow than the FFD method,and 34%–51%of computing time could be saved compared to the conventional CFD *** the choice of ventilation type,steady ventilation might result in short-circuit airflow and stagnant zones;alternatively,pulsating ventilation has greater potential in air contaminant removal due to its ever-changing vortex structure.

关键词： pulsating ventilation fast fluid dynamics fractional step method contaminant removal efficiency time-periodic supply vortex structure

CONVERGENCE OF CHORIN-MARSDEN FOR MULA FOR THENAVIER-STOKES EQUATIONS ON CONVEX DOMAINS

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Journal of Computational Mathematics 1999年第1期17卷 73-88页

作者： Lung-an Ying(Research institute for Mathematical Sciences, Kyoto University, Japan Department of Mathematics, Peking University, Beijing 100871, China) Peking Univ Dept Math Beijing 100871 Peoples R China Kyoto Univ Math Sci Res Inst Kyoto Japan

We prove the convergence of the Chorin-Marsden product formula for solving the initial-boundary value problems of the Navier-Stokes equations on convex domains. As a particular case we consider the case of the half pl... 详细信息

关键词： Navier Stokes equation vortex method fractional step method convergence

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 1-38页

作者： Yining CAO Mickaёl D.CHEKROUN Aimin HUANG Roger TEMAM Department of Mathematics and the Institute for Scientific Computing and Applied Mathematics Indiana University Department of Atmospheric and Oceanic Sciences University of California

The Jin-Neelin model for the El Nio–Southern Oscillation(ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO *** the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length k and on each sub-interval to solve successively the oceanic component, using the temperature T calculated on the previous sub-interval, to then solve the sea-surface temperature(SST for short) equation on the current sub-interval. The passage to the limit as k tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.

关键词： El Niño-Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems fractional step method Semigroup theory

High Order Compact Schemes in Projection methods for Incompressible Viscous Flows

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Communications in Computational Physics 2011年第4期9卷 994-1019页

作者： Michel Fournie Alain Rigal Institut de Mathematiques de Toulouse Universite de Toulouse et CNRS(UMR 5219)France

Within the projection schemes for the incompressible Navier-Stokes equations(namely"pressure-correction"method),we consider the simplest method(of order one in time)which takes into account the pressure in both steps of the splitting *** this scheme,we construct,analyze and implement a new high order compact spatial approximation on nonstaggered *** approach yields a fourth order accuracy in space with an optimal treatment of the boundary conditions(without error on the velocity)which could be extended to more general *** prove the unconditional stability of the associated Cauchy problem via von Neumann *** we carry out a normal mode analysis so as to obtain more precise results about the behavior of the numerical *** we present detailed numerical tests for the Stokes and the Navier-Stokes equations(including the driven cavity benchmark)to illustrate the theoretical results.

关键词： Incompressible Navier-Stokes fractional step method high order compact scheme boundary conditions

AN OPERATOR-SPLITTING ALGORITHM FOR ADVECTION-DIFFUSION-REACTION EQUATION

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Journal of Hydrodynamics 1992年第1期4卷 65-73页

作者： Cao Zhi-xian Wei Liang-yan Wuhan University of Hydraulic and Electric Engineering,Wuhan,Hubei 430072,P.R.China

An operator-splitting algorithm for three-dimensional advection-diffusion-reaction equation is *** method of characteristics is adopted for the pure advection operator, the explicit difference scheme is used for diffusion,and a prediction-correction scheme is em- ployed for *** condition for stability of the algorithm is *** inear and nonlinear examples are illustrated to test the convergence and accuracy of the numerical proce- dure,and satisfactory agreements between computed and analytical solutions are *** to its simplicity,stability,and validity for both one-and two-dimensional problems,the success- ful algorithm can be used to numerical simulations of viscous fluid flows,the transport of pollu- tants and sedimentations in reservoirs,lakes,rivers,estuaries and other environments,cooling- problems in heat or nuclear power plants,etc.

关键词： advection diffusion fractional step method stability method of characteristies numerical dispersion oscillating solution