# Pod Method In Pp Method

938 WordsAug 14, 20174 Pages
The simulations of reservoir are very important and have a wide range of applications, from ground-water production to radioactive waster and the extraction of oil and gas from the subsurface. 3D reservoir modelling provides more details for multiphase flows in porous media. However, the computational cost of 3D reservoir simulations is intensive. The non-intrusive reduced order modelling technique presented here is capable of resolving 3D reservoir modelling problems while avoiding the high computational cost. The reduced order modelling technique has been shown to possess a powerful capability of representing the large dynamical systems using only a few number of reduced order basis functions. Among the model reduction methods, the POD…show more content…
Another issue that arises in the ROMs is the efficient treatment of non-linear terms in the partial differential equations (PDEs). A number of efficient non-linear treatment methods have been presented, for example, Gappy POD \cite{willcox2006unsteady}, the empirical interpolation method (EIM)\cite{Barrault2004} and its discrete version discrete empirical interpolation method (DEIM) \cite{Chaturantabut2010}, residual DEIM \cite{Dxiao2014}, Petrov$-$Galerkin projection method \cite{Carlberg2011}, Gauss$-$Newton with approximated tensors (GNAT) method \cite{carlberg2013gnat} and the quadratic expansion method \cite{du2013pod,fang2009reduced}. However, these methods are still dependent on the source code of the original physical system. In most cases the source code describing the full physical system has to be modified in order to form the reduced order model. To circumvent these disadvantages, more recently, non-intrusive methods have been introduced into model reduction, which do not require the knowledge of the governing equations and the original source code \cite{han2012}. Chen {\it et al.} proposed a non-intrusive model reduction method based on black-box stencil interpolation method and machine learning method \cite{han2012}. Walton {\it et al.}proposed a non-intrusive reduced order technique for unsteady