Discretization methods with embedded analytical solutions for convection dominated transport in porous media

Authors:
Jürgen Geiser
Affiliations:
Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Venue:
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
Year:
2004

Citing 2
Cited 2

Discretization Methods with Discrete Minimum and Maximum Property for Convection Dominated Transport in Porous Media

NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Numerical Simulation of a Model for Transport and Reaction of Radionuclides

LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers

A domain decomposition method based on the iterative operator splitting method

Applied Numerical Mathematics
Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations

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Abstract

We will present a higher order discretization method for convection dominated transport equations. The discretisation for the convection-diffusion-reaction equation is based on finite volume methods which are vertex centered. The discretisation for the convection-reaction equation is improved with embedded analytical solutions for the mass. The method is based on the Godunovs-method, [10]. The exact solutions are derived for the one-dimensional convection- reaction equation with piecewise linear initial conditions. We introduce a special cases for the analytical solutions with equal reaction-parameters, confer [9]. We use operator-splitting for solving the convection-reaction-term and the diffusion-term. Numerical results are presented and compared the standard- with the modified- method. Finally we propose our further works on this topic.