Quasi-implicit treatment of velocity-dependent mobilities in underground porous media flow simulation

Quasi-implicit schemes for treating velocity-dependent mobilities in underground porous media flow simulation, occurring when modeling non-Newtonian and non-Darcy effects as well as capillary desaturation, are presented. With low-order finite-volume discretizations, the principle is to evaluate mobi...

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Vydáno v:Computational geosciences Ročník 25; číslo 1; s. 119 - 141
Hlavní autoři: Patacchini, Leonardo, de Loubens, Romain
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.02.2021
Springer Nature B.V
Témata:
Aquatic reptiles
Components
Desaturation
Earth and Environmental Science
Earth Sciences
Flow simulation
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Mathematical Modeling and Industrial Mathematics
Multiphase flow
Numerical stability
Original Paper
Porous media
Pressure gradients
Simulation
Soil Science & Conservation
Stability analysis
Three dimensional flow
Two dimensional flow
Velocity
Semi-implicit
Capillary desaturation
Quasi-implicit
Stability analysis
Non-Newtonian
Non-Darcy
ISSN:1420-0597, 1573-1499
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Shrnutí:Quasi-implicit schemes for treating velocity-dependent mobilities in underground porous media flow simulation, occurring when modeling non-Newtonian and non-Darcy effects as well as capillary desaturation, are presented. With low-order finite-volume discretizations, the principle is to evaluate mobilities at cell edges using normal velocity components calculated implicitly, and transverse velocity components calculated explicitly (i.e., based on the previously converged time-step); the pressure gradient driving the flow is, as usual, treated implicitly. On 3D hexahedral meshes, the proposed schemes require the same 7-point stencil as that of common semi-implicit schemes where mobilities are evaluated with an entirely explicit velocity argument. When formulated appropriately, their higher level of implicitness however places them, in terms of numerical stability, closer to “real” fully implicit schemes requiring at least a 19-point stencil. A von Neumann stability analysis of these proposed schemes is performed on a simplified pressure equation, representative of both single-phase and multiphase flows, following an approach previously used by the authors to study semi-implicit schemes. Whereas the latter are subject to stability constraints which limit their usage in certain cases where the logarithmic derivative of mobility with respect to velocity is large in magnitude, the former are unconditionally stable for 1D and 2D flows, and only subject to weak restrictionsfor 3D flows.
Bibliografie:ObjectType-Article-1
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ISSN:1420-0597
1573-1499
DOI:10.1007/s10596-020-09990-1