A non-linear finite volume method coupled with a modified higher order MUSCL-type method for the numerical simulation of two-phase flows in non-homogeneous and non-isotropic oil reservoirs

Contreras, Fernando Raul Licapa; Carvalho, Darlan Karlo Elisiário de; Galindez-Ramirez, G.; Lyra, Paulo Roberto Maciel

doi:10.1016/j.camwa.2021.03.023

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…The flux limiter updates the saturation in each mesh element such that its new element-wise average satisfies the maximum principle (11).…”

Section: Flux Limitermentioning

confidence: 99%

“…[6][7][8] On the other hand, finite volume methods are numerically diffusive and require Voronoi-type grids for unstructured meshes, which can be challenging to construct for anisotropic heterogeneous media. [9][10][11] DG methods overcome the shortcomings of finite volume methods because they belong to the class of variational problems like finite element methods. DG methods can be of arbitrary order, are adapted to any unstructured meshes, and in the case of convection-dominated problems, they produce sharp fronts with negligible numerical diffusion.…”

Section: Introductionmentioning

confidence: 99%

“…On the one hand, finite volume methods produce piecewise constant approximation of the saturation that satisfies physical bounds 6‐8 . On the other hand, finite volume methods are numerically diffusive and require Voronoi‐type grids for unstructured meshes, which can be challenging to construct for anisotropic heterogeneous media 9‐11 . DG methods overcome the shortcomings of finite volume methods because they belong to the class of variational problems like finite element methods.…”

Section: Introductionmentioning

confidence: 99%

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Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Sarraf Joshaghani,

Riviere

2023

Numerical Meth Engineering

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This paper presents a numerical study of immiscible, compressible two‐phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy and injection/production wells. We formulate a fully implicit stable discontinuous Galerkin solver for this system that is accurate, that respects maximum principle for the approximation of saturation, and that is locally mass conservative. To completely eliminate the overshoot and undershoot phenomena, we construct a flux limiter that produces bound‐preserving elementwise average of the saturation. The addition of a slope limiter allows to recover a pointwise bound‐preserving discrete saturation. Numerical results show that both maximum principle and monotonicity of the solution are satisfied. The proposed flux limiter does not impact the local mass error and the number of nonlinear solver iterations.

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“…The flux limiter updates the saturation in each mesh element such that its new element-wise average satisfies the maximum principle (11).…”

Section: Flux Limitermentioning

confidence: 99%