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Numerical Study of Natural Convection in an Inclined Porous Cavity

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Fluid Dynamics & Materials Processing 2022年第5期18卷 1389-1397页

作者： Saad Adjal Sabiha Aklouche-Benouaguef Belkacem Zeghmati Laboratoire des Transports Polyphasiques et Milieux Poreux LTPMPALGER16111ALGERIE Laboratoire des Mathématiques et Physique des Systèmes LAMPSPerpignan66860France

Two-dimensional transient laminar natural convection in a square cavity containing a porous medium and inclined at an angle of 30°is investigated numerically.The vertical walls are differentially heated,and the horizontal walls are adiabatic.The effect of Rayleigh number on heat transfer and on the road to chaos is analyzed.The natural heat transfer and the Darcy Brinkman equations are solved by using a finite volume method and a Tri Diagonal Matrix Algorithm(TDMA).The results are obtained for a porosity equal to 0.45,a Darcy number and a Prandtl respectively equal to 10^(-3)and 0.71;they are analyzed in terms of streamlines,isotherms,phase portrait,attractors,and spectra amplitude as a function of the Rayleigh number.It is found that,as Rayleigh number increases,the natural convection changes from a steady state to a time-periodic state and finally to a chaotic condition.

关键词： Natural convection porous medium finite volumes chaos attractors

Numerical Solution of 2-D Diffusion Problems Using Discrete Duality finite Volume Method on General Boundary Conditions

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Journal of Applied Mathematics and Physics 2022年第6期10卷 1968-1997页

作者： Hubert Donfack Aubin Kinfack Jeutsa Faculty of Science The University of Bamenda Bamenda Cameroon Higher Technical Teachers’ Training College The University of Buea Kumba Cameroon

In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.

关键词： Flow Problems Nonhomogeneous Anisotropic Media finite volumes Test Simulations

Boundary Conditions for Limited Area Models Based on the Shallow Water Equations

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Communications in Computational Physics 2013年第8期14卷 664-702页

作者： Arthur Bousquet Madalina Petcu Ming-Cheng Shiue Roger Temam Joseph Tribbia The Institute for Scientific Computing and Applied Mathematics Indiana UniversityBloomingtonIN 47405USA Laboratoire de Mathematiques et Applications UMR 6086Universite de PoitiersFrance The Institute of Mathematics of the Romanian Academy BucharestRomania Department of Applied Mathematics National Chiao Tung UniversityHsinchuTaiwan National Center for Atmospheric Research BoulderColoradoUSA.

A new set of boundary conditions has been derived by rigorousmethods for the shallow water equations in a limited domain.The aim of this article is to present these boundary conditions and to report on numerical simulations which have been performed using these boundary conditions.The new boundary conditions which are mildly dissipative let the waves move freely inside and outside the domain.The problems considered include a one-dimensional shallow water system with two layers of fluids and a two-dimensional inviscid shallow water system in a rectangle.

关键词： Boundary conditions finite volumes shallow water

Dispersive Shallow Water Wave Modelling.Part II:Numerical Simulation on a Globally Flat Space

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Communications in Computational Physics 2018年第1期23卷 30-92页

作者： Gayaz Khakimzyanov Denys Dutykh Oleg Gusev Nina Yu.Shokina Institute of Computational Technologies Siberian Branch of the Russian Academy of SciencesNovosibirsk 630090Russia LAMA UMR 5127 CNRSUniversitéSavoie Mont BlancCampus Scientifique73376 Le Bourget-du-Lac CedexFrance

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.

关键词： Nonlinear dispersive waves non-hydrostatic pressure moving adaptive grids finite volumes conservative finite differences

Colocated finite Volume Schemes for Fluid Flows

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Communications in Computational Physics 2008年第6期4卷 1-25页

作者： S.Faure J.Laminie R.Temam Laboratoire de Mathematiques Universite Paris-SudBatiment 42591405 OrsayFrance. GRIMAAG Guadeloupe Universite des Antilles et de la GuyaneCampus de FouilloleBP 59297157 Pointea Pitre CedexFrance. Institute for Scientific Computing and Applied Mathematics Indiana UniversityBloomingtonIN 47405USA.

Our aim in this article is to improve the understanding of the colocated finite volume schemes for the incompressible Navier-Stokes equations.When all the variables are colocated,that means here when the velocities and the pressure are computed at the same place(at the centers of the control volumes),these unknowns must be properly coupled.Consequently,the choice of the time discretization and the method used to interpolate the fluxes at the edges of the control volumes are essentials.In the first and second parts of this article,two different time discretization schemes are considered with a colocated space discretization and we explain how the unknowns can be correctly coupled.Numerical simulations are presented in the last part of the article.This paper is not a comparison between staggered grid schemes and colocated schemes(for this,see,e.g.,[15,22]).We plan,in the future,to use a colocated space discretization and the multilevel method of[4]initially applied to the two dimensional Burgers problem,in order to solve the incompressible Navier-Stokes equations.One advantage of colocated schemes is that all variables share the same location,hence,the possibility to use hierarchical space discretizations more easily when multilevel methods are used.For this reason,we think that it is important to study this family of schemes.

关键词： finite volumes colocated scheme.

The Algebraic Immersed Interface and Boundary Method for Elliptic Equations with Jump Conditions

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Open Journal of Fluid Dynamics 2020年第3期10卷 239-269页

作者： Arthur Sarthou Stéphane Vincent Philippe Angot Jean-Paul Caltagirone Buf Compagnie Paris France Laboratoire MSME Université Gustave Eiffel Champs-sur-Marne France Institut de Mathématiques de Marseille Centrale Marseille Marseille France Institut Polytechnique de Bordeaux Université de Bordeaux Talence France

A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.

关键词： Fictitious Domain Immersed Interface Method Immersed Boundary Method Penalty Methods finite volumes Elliptic Equations Jump Embedded Conditions