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Journal of Scientific Computing

, Volume 38, Issue 1, pp 50–73 | Cite as

Unified Formulation for High-Order Streamline Tracing on Two-Dimensional Unstructured Grids

  • Ruben Juanes
  • Sébastien F. Matringe
Article

Abstract

Accurate streamline tracing and travel time computation are essential ingredients of streamline methods for groundwater transport and petroleum reservoir simulation. In this paper we present a unified formulation for the development of high-order accurate streamline tracing algorithms on unstructured triangular and quadrilateral grids. The main result of this paper is the identification of velocity spaces that are suitable for streamline tracing. The essential requirement is that the divergence-free part of the velocity must induce a stream function. We recognize several classes of velocity spaces satisfying this requirement from the theory of mixed finite element methods and, for each class, we obtain the precise functional form of the stream function. Not surprisingly, the most widely used tracing algorithm (Pollock’s method) emanates in fact from the lowest-order admissible velocity approximation. Therefore, we provide a sound theoretical justification for the low-order algorithms currently in use, and we show how to achieve higher-order accuracy both in the streamline tracing and the travel time computation.

Keywords

Streamline methods Streamline tracing Mixed finite elements Stream function Darcy flow Groundwater Petroleum reservoir simulation 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dept. of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Dept. of Energy Resources EngineeringStanford UniversityStanfordUSA

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