A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

Salinas, P.; Pavlidis, Dimitrios; Xie, Zhihua; Osman, H.; Pain, Christopher C.; Jackson, Matthew D.

doi:10.1016/j.jcp.2017.09.058

Cited by 33 publications

(20 citation statements)

References 42 publications

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“…The collection of surrogates {f s } N s s=1 can be constructed a priori and stored as a collection of RBF coefficients. For a generic system state , N s values of f s ( ) are cheaply evaluated first (18) and their values are stored. Next, a new surrogate dependent on parameterization only is constructed locally (for this specific ) from…”

Section: Previous Approachmentioning

confidence: 99%

“…The second multiphase flow problem investigated is a reconstruction of the Edward's model studied in References 7,18. In this example the 2D square domain exhibits a degree of heterogeneity by including four barriers ( Figure 10), with each barrier characterized by the isotropic permeability value between 10 −4 and 10 2 relatively to the red background. We point out that the permeability range used in this study is much wider than in Reference 7 and leads to a nontrivial range of flow patterns (Figure 11), not present if the original range is used.…”

Section: Four Barriers Casementioning

confidence: 99%

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An efficient and robust method for parameterized nonintrusive reduced‐order modeling

Kostorz

Muggeridge

Jackson

2020

Numerical Meth Engineering

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Summary A method of constructing parameterized nonintrusive reduced‐order models (NIROMs) is given. The approach relies on a geometrical interpretation of NIROM, requires only a single layer of interpolation to be applied for both system state and parametric dependence of the model and is applicable to systems characterized by any number of parameters spanning arbitrary orders of magnitude. The method is applied to three representative test problems and evaluated in terms of accuracy and speed, showing good performance.

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Section: Previous Approachmentioning

confidence: 99%

Section: Four Barriers Casementioning

confidence: 99%

An efficient and robust method for parameterized nonintrusive reduced‐order modeling

Kostorz

Muggeridge

Jackson

2020

Numerical Meth Engineering

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“…7d using a fine, fixed mesh, DMO every time-step and DMO within the non-linear solver Fig. 9 a Number of non-linear iterations per time-step for the first 18 time-steps for the test case 4.1; the runtime of this simulation is 220 s. b Number of elements per time-step for the first 18 time-steps; the runtime of this simulation is 230 s been developed to try to solve this problem ( [1,6,34,35,41]); here, the dispersion is reduced by using DMO. The effect of the high viscosity appears with a less sharp leading shock-front.…”

Section: D High Permeability Inclusion In a Low Permeability Regionmentioning

confidence: 99%

A robust mesh optimisation method for multiphase porous media flows

et al. 2018

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Flows of multiple fluid phases are common in many subsurface reservoirs. Numerical simulation of these flows can be challenging and computationally expensive. Dynamic adaptive mesh optimisation and related approaches, such as adaptive grid refinement can increase solution accuracy at reduced computational cost. However, in models or parts of the model domain, where the local Courant number is large, the solution may propagate beyond the region in which the mesh is refined, resulting in reduced solution accuracy, which can never be recovered. A methodology is presented here to modify the mesh within the non-linear solver. The method allows efficient application of dynamic mesh adaptivity techniques even with high Courant numbers. These high Courant numbers may not be desired but a consequence of the heterogeneity of the domain. Therefore, the method presented can be considered as a more robust and accurate version of the standard dynamic mesh adaptivity techniques.

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“…Several methods have been used to simulate two-phase flow, such as the finite element method, 2 the finite volume method, [2][3][4][5] mixed finite element methods, 2,6,7 and discontinuous Galerkin methods. 2,[8][9][10][11][12][13][14][15][16][17] Recently, many efforts have been focused on applying high-order methods to these kind of problems due to their advantages.…”

Section: Introductionmentioning

confidence: 99%

High‐order hybridizable discontinuous Galerkin formulation with fully implicit temporal schemes for the simulation of two‐phase flow through porous media

Costa-Solé

Ruiz‐Gironés

Sarrate

2021

Numerical Meth Engineering

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We present a memory-efficient high-order hybridizable discontinuous Galerkin (HDG) formulation coupled with high-order fully implicit Runge-Kutta schemes for immiscible and incompressible two-phase flow through porous media. To obtain the same high-order accuracy in space and time, we propose using high-order temporal schemes that allow using large time steps. Therefore, we require unconditionally stable temporal schemes for any combination of element size, polynomial degree, and time step. Specifically, we use the Radau IIA and Gauss-Legendre schemes, which are unconditionally stable, achieve high-order accuracy with few stages, and do not suffer order reduction in this problem. To reduce the memory footprint of coupling these spatial and temporal high-order schemes, we rewrite the nonlinear system. In this way, we achieve a better sparsity pattern of the Jacobian matrix and less coupling between stages. Furthermore, we propose a fix-point iterative method to further reduce the memory consumption. The saturation solution may present sharp fronts. Thus, the high-order approximation may contain spurious oscillations.To reduce them, we introduce artificial viscosity. We detect the elements with high-oscillations using a computationally efficient shock sensor obtained from the saturation solution and the post-processed saturation of HDG. Finally, we present several examples to assess the capabilities of our formulation.

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A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

Cited by 33 publications

References 42 publications

An efficient and robust method for parameterized nonintrusive reduced‐order modeling

An efficient and robust method for parameterized nonintrusive reduced‐order modeling

A robust mesh optimisation method for multiphase porous media flows

High‐order hybridizable discontinuous Galerkin formulation with fully implicit temporal schemes for the simulation of two‐phase flow through porous media

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