Displaying similar documents to “Maximum principle and local mass balance for numerical solutions of transport equation coupled with variable density flow.”

Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications

Jürgen Geiser (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We...

Contaminant transport with adsorption in dual-well flow

Jozef Kačur, Roger Van Keer (2003)

Applications of Mathematics

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Numerical approximation schemes are discussed for the solution of contaminant transport with adsorption in dual-well flow. The method is based on time stepping and operator splitting for the transport with adsorption and diffusion. The nonlinear transport is solved by Godunov’s method. The nonlinear diffusion is solved by a finite volume method and by Newton’s type of linearization. The efficiency of the method is discussed.

On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Vít Dolejší, Miloslav Feistauer, Christoph Schwab (2002)

Mathematica Bohemica

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The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined...

Transport of pollutant in shallow water : a two time steps kinetic method

Emmanuel Audusse, Marie-Odile Bristeau (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The aim of this paper is to present a finite volume kinetic method to compute the transport of a passive pollutant by a flow modeled by the shallow water equations using a new time discretization that allows large time steps for the pollutant computation. For the hydrodynamic part the kinetic solver ensures – even in the case of a non flat bottom – the preservation of the steady state of a lake at rest, the non-negativity of the water height and the existence of an entropy inequality....

Ecological modeling and Lagrangian approach

Boris Arkhipov, Viacheslav Solbakov, Mikhail Solov’ev, Dmitry Shapochkin (2013)

Open Mathematics

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A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the...

Conservation schemes for convection-diffusion equations with Robin boundary conditions

Stéphane Flotron, Jacques Rappaz (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energy for a heat equation or the total mass of a solute in a fluid for a concentration equation, even if the approximation of the velocity field is not completely divergence-free. We establish a priori errror estimates for this scheme and...