Streamline methods have received renewed interest over thernpast decade as an attractive alternative to traditional finiterndifference simulation. They have been applied successfully torna wide range of problems including production optimization,rnhistory matching and upscaling. Streamline methods are alsornbeing extended to provide an efficient and accurate tool forrncompositional reservoir simulation. One of the keyrncomponents in a streamline method is the streamline tracingrnalgorithm. Traditionally, streamlines were traced on regularrnCartesian grids using Pollock's method. Several extensions torndistorted or unstructured rectangular, triangular and polygonalrngrids have been proposed. All of these formulations are,rnhowever, low-order schemes.rnHere we propose a unified formulation for high-orderrnstreamline tracing on unstructured quadrilateral and triangularrngrids, based on the use of the stream function. Starting fromrnthe theory of mixed finite element methods, we identifyrnseveral classes of velocity spaces that induce a stream functionrnand are therefore suitable for streamline tracing. In doing so,rnwe provide a theoretical justification for the low-orderrnmethods currently in use, and we show how to extend them tornachieve high-order accuracy. Consequently, our streamlinerntracing algorithm is semi-analytical: within each gridblock thernstreamline is traced exactly. We give a detailed description ofrnthe implementation of the algorithm and we provide arncomparison of low- and high-order tracing methods by meansrnof representative numerical simulations on two-dimensionalrnheterogeneous media.
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