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A high‐order TVD transport method for hybrid meshes on complex geological geometry
Author(s) -
Matthäi S. K.,
Mezentsev A. A.,
Pain C. C.,
Eaton M. D.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.901
Subject(s) - discretization , polygon mesh , courant–friedrichs–lewy condition , mathematics , total variation diminishing , geometry , parametric statistics , multiphase flow , mathematical optimization , mathematical analysis , mechanics , physics , statistics
The paper presents a new implicit pressure–implicit saturation higher‐order accurate in space and second‐order accurate in time advection–dispersion scheme for the hyperbolic transport equations in porous media with discrete three‐dimensional representation of material interfaces. We develop adaptive time differencing methods to use time steps greater than the mesh Courant number (Courant–Friedrich–Levy condition, CFL). The paper pays special attention to hybrid discretization of subsurface geometry, placing emphasis on the multiphase flow in fractured petroleum reservoirs. We also introduce numerical iso‐parametric double mapping integration method for node‐centred hybrid meshes and use it in our transport scheme. Copyright © 2005 John Wiley & Sons, Ltd.