Abstract
We investigate time stepping schemes for the adaptive cell-centered finite volume solution of diffusion equations with heterogeneous diffusion coefficients. The proposed finite volume method uses the cell-centered techniques to discretize the diffusion operators on unstructured grids. Explicit and implicit time integration schemes are used and a comparative study is presented in terms of accuracy and efficiency. Numerical results are presented for a transient diffusion equation with known analytical solution. We also apply these methods to a problem of oil recovery using a two-phase flow problem in porous media.
MSC2010: 76S05, 65N08, 65Y20
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© 2011 Springer-Verlag Berlin Heidelberg
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Benkhaldoun, F., Mahamane, A., Seaïd, M. (2011). Adaptive cell-centered finite volume method for non-homogeneous diffusion problems: Application to transport in porous media. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_9
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DOI: https://doi.org/10.1007/978-3-642-20671-9_9
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