Abstract
In this work we derive a numerical technique based on finite-difference WENO schemes for the simulation of multi-dimensional multiphase flows in a homogeneous porous medium. The key idea is to define a compatible discretization for the fluxes of the convective term in order to maintain their divergence-free character not only in the continuous setting but also in the discrete setting, ensuring the conservation of the sum of the saturations through time evolution. The one-dimensional numerical technique is derived in detail for the case of neglected capillarity effects. Numerical results obtained with one-dimensional and two-dimensional standard tests of multiphase flow in a homogeneous porous medium are shown.
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Acknowledgements
This research was partially supported by Ministerio de Economía y Competitividad under grant MTM2011-22741 and MTM2014-54388-P with the participation of FEDER. M.C. Martí and R. Bürger acknowledge support by CONICYT Postdoctoral 2015 Fondecyt project 3150140. R. Bürger acknowledges support by Fondecyt project 1130154; Conicyt project Anillo ACT1118 (ANANUM); Red Doctoral REDOC.CTA, MINEDUC project UCO1202 at Universidad de Concepción; BASAL project CMM, Universidad de Chile and Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción; and Centro CRHIAM Proyecto Conicyt Fondap 15130015.
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Bürger, R., Guerrero, F., Martí, M.C., Mulet, P. (2016). WENO Schemes for Multi-Dimensional Porous Media Flow Without Capillarity. In: Ortegón Gallego, F., Redondo Neble, M., Rodríguez Galván, J. (eds) Trends in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-32013-7_17
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