Hybrid upwind discretization of nonlinear two-phase flow with gravity

Lee, S.H.; Efendiev, Yalchin; Tchelepi, Hamdi A.

doi:10.1016/j.advwatres.2015.04.007

Cited by 52 publications

(33 citation statements)

References 18 publications

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“…We complement the analysis from [19] by performing refinement studies illustrating that the IHU and PPU schemes converge to the same solution. Two-phase flow.…”

Section: Saturation Estimatementioning

confidence: 99%

“…We extended the finite-volume discretization based on hybrid upwinding [19] from two phases to an arbitrary number of phases. Summary of results and conclusions.…”

Section: Refinement In Time Only the Initial Condition For This Testmentioning

confidence: 99%

“…Recently, Lee, Efendiev, and Tchelepi [19] dealt with the strong coupling between the viscous and buoyancy forces for two-phase flow with an implicit TPFA finitevolume scheme that retains the simplicity of PPU. They presented a hybrid upwinding scheme applied to the transport equation, in which the upwinding of the viscous part of the numerical flux is based on the total velocity, whereas the approximation of the buoyancy term is fully determined by fluid densities such that the heaviest fluid goes down and the lightest fluid goes up.…”

mentioning

confidence: 99%

“…Next, we propose a generalization of the finite-volume hybrid upwinding [19] for transport to an arbitrary number of fluid phases.…”

mentioning

confidence: 99%

“…We first extend the finite-volume hybrid upwinding for two-phase flow [19] to three, or more, phases. Implicit hybrid upwinding (IHU).…”

mentioning

confidence: 99%

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Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

Hamon¹

2016

SIAM J. Numer. Anal.

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The systems of algebraic equations arising from implicit (backward-Euler) finitevolume discretization of the conservation laws governing multiphase flow in porous media are quite challenging for nonlinear solvers. In the presence of countercurrent flow due to buoyancy, the numerical flux obtained with single-point Phase-Potential Upwinding (PPU) is not differentiable, which causes convergence difficulties for nonlinear solvers. Recently, [Lee, Efendiev, and Tchelepi, Adv. Water Resour., 82 (2015), pp. 27-38] proposed a hybrid upwinding strategy for two-phase flow that gives rise to a differentiable numerical flux across the entire viscous-gravity parameter space. Here, we first present an Implicit Hybrid Upwinding (IHU) scheme for hyperbolic conservation laws, extending the work of Lee, Efendiev, and Tchelepi to an arbitrary number of fluid phases. We show that the numerical flux obtained with the IHU is consistent, and a monotone function of its own saturation. It is also a differentiable function of the saturations in one spatial dimension. In addition, we generalize the IHU numerical scheme to solve the elliptic-hyperbolic partial differential equations governing coupled flow and transport in multiple dimensions. For this problem, we derive pressure and saturation estimates, and prove the existence of a solution to the scheme. Finally, we apply the IHU scheme to the Buckley-Leverett problem with buoyancy. Our numerical experiments confirm that IHU is nonoscillatory, convergent, and improves upon Newton's method convergence rate for two-and three-phase flow.

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“…We complement the analysis from [19] by performing refinement studies illustrating that the IHU and PPU schemes converge to the same solution. Two-phase flow.…”

Section: Saturation Estimatementioning

confidence: 99%

“…We extended the finite-volume discretization based on hybrid upwinding [19] from two phases to an arbitrary number of phases. Summary of results and conclusions.…”

Section: Refinement In Time Only the Initial Condition For This Testmentioning

confidence: 99%

mentioning

confidence: 99%

“…Next, we propose a generalization of the finite-volume hybrid upwinding [19] for transport to an arbitrary number of fluid phases.…”

mentioning

confidence: 99%

“…We first extend the finite-volume hybrid upwinding for two-phase flow [19] to three, or more, phases. Implicit hybrid upwinding (IHU).…”

mentioning

confidence: 99%

See 3 more Smart Citations

Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

Hamon¹

2016

SIAM J. Numer. Anal.

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show abstract

Successful application of multiscale methods in a real reservoir simulator environment

et al. 2017

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Nonlinear solver for three-phase transport problems based on approximate trust regions

Møyner

2017

Comput Geosci

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Hybrid upwind discretization of nonlinear two-phase flow with gravity

Cited by 52 publications

References 18 publications

Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

Analysis of Hybrid Upwinding for Fully-Implicit Simulation of Three-Phase Flow with Gravity

Successful application of multiscale methods in a real reservoir simulator environment

Nonlinear solver for three-phase transport problems based on approximate trust regions

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