Multilevel Adaptive Modeling Of Multiphase Flow In Porous Media
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H. Gotovac, R. Andričević, B. Gotovac, M. Vranješ & T. Radelja
Multiphase flow in porous media is characterized by zones of sharp gradients that include the development of sharp interfaces and narrow transition zones. Numerical modeling of these problems usually shows difficulties in resolving all space and temporal scales, numerical oscillations and artificial dispersion and obviously needs a demanding computational request with very fine grid and small time steps. Adaptive numerical modeling is one of the most promising options. In the last decade adaptive collocation methods have become very popular due to using a highly localized basis functions as wavelets or splines. In this paper we present the lesser-known localized Fup (Finite up function) basis functions with compact support and Adaptive Fup Collocation Method (AFCM) appropriate for application to multiphase flow problems in porous media. The numerical procedure is designed through a well-known method of lines (MOL). Space discretization and grid adaptation are obtained by Fup collocation transform and corresponding adaptive strategy, while time integration is reduced to a solving system of differential-algebraic equations. Furthermore, the method enables an adaptive multilevel evolution of a solution with all resolved spatial and temporal scales and desired level of accuracy using the whole family of Fup basis functions. The numerical method is tested and verified with classic Buckley-Leverett 1-D multiphase flow problem in porous media. Keywords: atomic functions, Fup basis functions, method of lines, adaptive collocation method, multiresolution approach, multiphase flow in porous media. 1 Introduction Many physical and engineering problems exhibit a wide range of space and/or temporal scales. Moreover, lot of variables associated to these problems show
atomic functions, Fup basis functions, method of lines, adaptivecollocation method, multiresolution approach, multiphase flow in porous media.