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Robust Multi-D Transport Schemes with Reduced Grid Orientation Effects

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In this paper we investigate truly multi-D upwind schemes for simulating adverse mobility ratio displacements in porous media. Due to an underlying physical instability at the simulation scale, numerical results are highly sensitive to discretization errors and hence the orientation of the underlying computational grid. We use modified equations analysis to predict preferred flow angles on structured grids for several popular methods and present a conservative, multi-D framework for designing positive upwind schemes for general velocity fields. After placing the common schemes in this framework, we go on to develop a novel scheme with “minimal” constant transverse (cross-wind) diffusion. Results for miscible gas injection into homogeneous and heterogeneous media demonstrate that truly multi-D schemes, and in particular our new scheme, greatly reduce grid orientation effects and numerical biasing as compared to dimensional upwinding.

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Correspondence to Jeremy Kozdon.

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Kozdon, J., Mallison, B. & Gerritsen, M. Robust Multi-D Transport Schemes with Reduced Grid Orientation Effects. Transp Porous Med 78, 47–75 (2009).

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  • Multi-D transport
  • Grid orientation effect
  • Adverse mobility ratio
  • Miscible gas injection
  • Physical instabilities
  • Interaction regions
  • Positivity
  • Hyperbolic equations
  • Finite volume
  • Finite difference