Multilevel Adaptive Modeling Of
Multiphase Flow In Porous Media
Author(s)
H. Gotovac, R. Andričević, B. Gotovac, M. Vranješ & T. Radelja
Abstract
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
Keywords
atomic functions, Fup basis functions, method of lines, adaptivecollocation method, multiresolution approach, multiphase flow in porous media.
Related Book
Other papers in this volume
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