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AViscosity-Splitting method for the Navier-Stokes/ Darcy Problem

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 251-277页

作者： Yunxia Wang Xuefeng Han Zhiyong Si School of Materials Science and Engineering Henan Polytechnic UniversityJiaozuoHenan 454003China Henan Joint International Research Laboratory for High Performance Metallic Material and Their Numerical Simulation Henan Polytechnic UniversityJiaozuoHenan 454003China School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuoHenan 454003China School of Mathematics and Computational Science Xiangtan UniversityXiangtanHunan 411105China

In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy *** this method,the Navier-Stokes/Darcy equation is solved in three *** the first step,an explicit/implicit formulation is used to solve the nonlinear *** introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter *** the second step,we solve the Stokes equation for velocity and *** the third step,we solve the Darcy equation for the piezometric head in the porous media *** use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s *** stability analysis,under some condition △t≤k0,k0>0,is *** error estimates prove our method has an optimal convergence ***,some numerical results are presented to show the performance of our algorithm.

关键词： Navier-Stokes/Darcy equations fractional step method viscosity-splitting method,stability analysis optimal error analysis

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

Mathematical Analysis of the Jin-Neelin Model of El Nio-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 Nio–Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems fractional step method Semigroup theory

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.

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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

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

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

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