Multiscale HDG model reduction method for flows in heterogeneous porous media

Moon, Minam; Lazarov, Raytcho; Jun, Hyung Kyu

doi:10.1016/j.apnum.2019.01.011

Cited by 5 publications

(1 citation statement)

References 27 publications

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“…Darcy flow and two-phase flow simulations in highly heterogeneous media are performed in [270] via the so-called generalised multiscale HDG (GMsHDG) method which is connected to the mortar mixed finite element method described in [24]. GMsHDG was also employed for multiscale simulations of elliptic PDEs in heterogeneous media [70,123] and perforated domains [65] and of parabolic PDEs in heterogeneous media [192].…”

Section: Two-phase Flows and Heterogeneous Porous Mediamentioning

confidence: 99%

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Giacomini

Sevilla

Huerta

2020

Arch Computat Methods Eng

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This paper presents , an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in . Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator is provided to facilitate its application to practical engineering problems.

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Section: Two-phase Flows and Heterogeneous Porous Mediamentioning

confidence: 99%

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Giacomini

Sevilla

Huerta

2020

Arch Computat Methods Eng

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Hybridizable discontinuous Galerkin method with mixed-order spaces for non-linear diffusion equations with internal jumps

et al. 2023

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We formulate a hybridizable discontinuous Galerkin method for parabolic equations with non-linear tensor-valued coefficients and jump conditions (Henry’s law). The analysis of the proposed scheme indicates the optimal convergence order for mildly non-linear problems. The same order is also obtained in our numerical studies for simplified settings. A series of numerical experiments investigate the effect of choosing different order approximation spaces for various unknowns.

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Generalized multiscale hybridizable discontinuous Galerkin (GMsHDG) method for flows in nonlinear porous media

Moon

2022

Journal of Computational and Applied Mathematics

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Multiscale HDG model reduction method for flows in heterogeneous porous media

Cited by 5 publications

References 27 publications

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

Hybridizable discontinuous Galerkin method with mixed-order spaces for non-linear diffusion equations with internal jumps

Generalized multiscale hybridizable discontinuous Galerkin (GMsHDG) method for flows in nonlinear porous media

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