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.
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Geiser, J. (2005). Discretization Methods with Embedded Analytical Solutions for Convection Dominated Transport in Porous Media. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_34
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DOI: https://doi.org/10.1007/978-3-540-31852-1_34
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