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Discretization Methods with Embedded Analytical Solutions for Convection Dominated Transport in Porous Media

  • Jürgen Geiser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3401)

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.

Keywords

Discretization Method Dual Mesh Local Time Step Splitting Error Double Porosity Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jürgen Geiser
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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