Multidimensional upstream weighting for multiphase transport on general grids

Keilegavlen, Eirik; Kozdon, Jeremy E.; Mallison, Bradley T.

doi:10.1007/s10596-012-9301-7

Cited by 33 publications

(16 citation statements)

References 31 publications

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“…A similar monotonicity condition is used in Kozdon et al (2011a); Keilegavlen et al (2012). In Section 5, we use this property to show that the saturation solution of the fully implicit scheme remains between physical bounds, 0 and 1.…”

Section: Flux Approximationmentioning

confidence: 99%

“…The weights given to the upwind volumes are chosen to improve accuracy by accounting for characteristic information while also honoring monotonicity. To define this stencil, we adapt the approach previously used in Kozdon et al (2011a); Keilegavlen et al (2012) and use a dual grid made of the union of interaction regions as illustrated in Fig. 1.…”

Section: Integration Region Frameworkmentioning

confidence: 99%

“…In this work, we limit the scope of the numerical study to Cartesian grids with scalar permeability and therefore exclusively consider a Two-Point Flux Approximation (TPFA) to compute this transmissibility term. Multi-Point Flux Approximations (MPFA, Aavatsmark et al, 1998;Edwards and Rogers, 1998;Aavatsmark, 2002;Zhou et al, 2011) are required for more general cases as previously shown by Keilegavlen et al (2012); Lamine and Edwards (2013); Souza et al (2018). Considering half interface Γ (m) k+1/2 between vertices k and k + 1, we define the rock-and geometric transmissibility as…”

Section: Flux Approximationmentioning

confidence: 99%

“…We first assess the reduction of the numerical bias caused by the orientation of the grid with a threewell problem with buoyancy derived from Kozdon et al (2011a); Keilegavlen et al (2012). We consider a x − y domain of dimensions [−0.5 ft, 0.5 ft] × [−0.5 ft, 0.5 ft], discretized with a 51 × 51 uniform Cartesian grid so that ∆x = ∆y = 1/51 ft.…”

Section: Three-well Problem With Buoyancymentioning

confidence: 99%

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Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

Hamon

Mallison

2020

Computer Methods in Applied Mechanics and Engineering

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Robust and accurate fully implicit finite-volume schemes applied to Darcy-scale multiphase flow and transport in porous media are highly desirable. Recently, a smooth approximation of the saturationdependent flux coefficients based on Implicit Hybrid Upwinding (IHU) has been proposed to improve the nonlinear convergence in fully implicit simulations with buoyancy. Here, we design a truly multidimensional extension of this approach that retains the simplicity and robustness of IHU while reducing the sensitivity of the results to the orientation of the computational (Cartesian) grid. This is achieved with the introduction of an adaptive, local coupling between the fluxes that takes the flow pattern into account. We analyze the mathematical properties of the proposed methodology to show that the scheme is monotone in the presence of competing viscous and buoyancy forces and yields saturations remaining between physical bounds. Finally, we demonstrate the efficiency and accuracy of the scheme on challenging two-dimensional two-phase examples with buoyancy, with an emphasis on the reduction of the grid orientation effect.

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Section: Flux Approximationmentioning

confidence: 99%

Section: Integration Region Frameworkmentioning

confidence: 99%

Section: Flux Approximationmentioning

confidence: 99%

Section: Three-well Problem With Buoyancymentioning

confidence: 99%

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Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

Hamon

Mallison

2020

Computer Methods in Applied Mechanics and Engineering

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“…Standard formulations for upstream weighting used in porous media follow those for hyperbolic conservation laws [23], or their multi-dimensional generalizations [24].…”

Section: Spatial Discretizationmentioning

confidence: 99%

A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

Radu

Nordbotten

Pop

et al. 2015

Journal of Computational and Applied Mathematics

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a b s t r a c tIn this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results.

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A generic workflow of projection-based embedded discrete fracture model for flow simulation in porous media

Rao

2023

Comput Geosci

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Multidimensional upstream weighting for multiphase transport on general grids

Cited by 33 publications

References 31 publications

Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

Fully Implicit multidimensional Hybrid Upwind scheme for coupled flow and transport

A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

A generic workflow of projection-based embedded discrete fracture model for flow simulation in porous media

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