Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media

Cheng, Hanz Martin; Droniou, Jérôme; Le, Kim Ngan

doi:10.1007/s00211-018-1002-2

Cited by 6 publications

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“…Analysis of an ELLAM-MFEM for (1.1)-(1.3) was presented in [49,50]. A more general ELLAM scheme was proposed and investigated in the recent work [11]. The convergence rate of the method in spatial direction is similar to those in (1.5) and (1.7).…”

Section: Introductionmentioning

confidence: 86%

Analysis of lowest-order characteristics-mixed FEMs for incompressible miscible flow in porous media

Sun¹

2022

Preprint

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The time discrete scheme of characteristics type is especially effective for convectiondominated diffusion problems. The scheme has been used in various engineering areas with different approximations in spatial direction. The lowest-order mixed method is the most popular one for miscible flow in porous media. The method is based on a linear Lagrange approximation to the concentration and the zero-order Raviart-Thomas approximation to the pressure/velocity. However, the optimal error estimate for the lowest-order characteristicsmixed FEM has not been presented although numerous effort has been made in last several decades. In all previous works, only first-order accuracy in spatial direction was proved under certain time-step and mesh size restrictions. The main purpose of this paper is to establish optimal error estimates, i.e., the second-order in L 2 -norm for the concentration and the first-order for the pressure/velocity, while the concentration is more important physical component for the underlying model. For this purpose, an elliptic quasi-projection is introduced in our analysis to clean up the pollution of the numerical velocity through the nonlinear dispersion-diffusion tensor and the concentration-dependent viscosity. Moreover, the numerical pressure/velocity of the second-order accuracy can be obtained by re-solving the (elliptic) pressure equation at a given time level with a higher-order approximation. Numerical results are presented to confirm our theoretical analysis.

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Section: Introductionmentioning

confidence: 86%

Analysis of lowest-order characteristics-mixed FEMs for incompressible miscible flow in porous media

Sun¹

2022

Preprint

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“…Moreover, this idea is easily applicable in both 2D and 3D. Upon working on the assumption that each ball, when tracked, remains a ball, the points C K,s are then tracked by solving (10) to obtain \widehat C K,s , which will be treated as the center of the tracked ball \widehat B K,s (see Figure 2). Of course, this assumption is not true in general but gives a good approximation of the volumes, especially if the initial Downloaded 04/15/20 to 131.155.76.193.…”

Section: Remark 23 (Reconstruction Of Polytopes)mentioning

confidence: 99%

“…As in [9], we describe the numerical method in a general setting, to ensure that our algorithm applies at once to various possible spatial discretizations for the diffusion terms in (2). These can be dealt with using the GDM as shown in [9,10] and will not be discussed in further detail for this paper. We replace, in the weak formulation of the model, the continuous (infinite-dimensional) spaces and corresponding operators by a discrete (finite-dimensional) space and function reconstructions.…”

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confidence: 99%

“…Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php Define the flow F t : \Omega \rightar \Omega such that, for a.e. \bfitx \in \Omega , (10) dF t (\bfitx )…”

mentioning

confidence: 99%

“…Under assumptions (3) and 5, the existence of this flow is proved in [10,Lemma 5.1]. The solution to (9) is then understood in the sense that for t \in (t (n) , t (n+1) ] and a.e.…”

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confidence: 99%

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An Efficient Implementation of Mass Conserving Characteristic-Based Schemes in Two and Three Dimensions

Cheng

Droniou

2020

SIAM J. Sci. Comput.

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New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous media

Sun

2021

Numer. Math.

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Convergence analysis of a family of ELLAM schemes for a fully coupled model of miscible displacement in porous media

Cited by 6 publications

References 28 publications

Analysis of lowest-order characteristics-mixed FEMs for incompressible miscible flow in porous media

Analysis of lowest-order characteristics-mixed FEMs for incompressible miscible flow in porous media

An Efficient Implementation of Mass Conserving Characteristic-Based Schemes in Two and Three Dimensions

New analysis and recovery technique of mixed FEMs for compressible miscible displacement in porous media

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