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)


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.


Discretization Method Dual Mesh Local Time Step Splitting Error Double Porosity Medium 
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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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