Arbitrary Lagrangian–Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces

Fu, Guosheng

doi:10.1016/j.cma.2020.113158

Cited by 13 publications

(4 citation statements)

References 61 publications

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“…This is achieved by static condensation. Since its introduction, many HDG methods for incompressible flows have been introduced, 32‐39 as well as various ALE‐HDG methods for problems on moving domains 13,40,41 …”

Section: Introductionmentioning

confidence: 99%

A conforming sliding mesh technique for an embedded‐hybridized discontinuous Galerkin discretization for fluid‐rigid body interaction

Horváth

Rhebergen

2022

Numerical Methods in Fluids

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In previous work, we introduced a space-time embedded-hybridizable discontinuous Galerkin method for the solution of the incompressible Navier-Stokes equations on time-dependent domains of which the motion of the domain is prescribed. This discretization is exactly mass conserving, locally momentum conserving, and energy-stable. In this article, we extend this discretization to fluid-rigid body interaction problems in which the motion of the fluid domain is not known a priori. To account for large rotational motion of the rigid body, we present a novel conforming space-time sliding mesh technique. For this we introduce a local edge swapping algorithm such that the global mesh of a space-time slab is one of only four different configurations. These configurations can be pre-computed thereby reducing any costs associated with changing mesh connectivity. Furthermore, edge swapping occurs only within the space-time slab between the discrete time-levels; there is no edge swapping on spatial meshes and so there is no need to project the solution from one spatial mesh to another. We demonstrate the performance of the discretization on various numerical examples.

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Section: Introductionmentioning

confidence: 99%

A conforming sliding mesh technique for an embedded‐hybridized discontinuous Galerkin discretization for fluid‐rigid body interaction

Horváth

Rhebergen

2022

Numerical Methods in Fluids

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“…More precisely, stemming from the HDG formulation introduced in [222], H(div)-conforming hybridised DG [160] and EHDG [161] methods were proposed. Hybridised DG and HDG methods with arbitrary Lagrangian Eulerian (ALE) formulations were thus presented in [134,140] and the resulting HDG-ALE framework was applied to fluid-structure interaction (FSI) problems involving incompressible [248] and weakly-compressible flows [176].…”

Section: Incompressible Flowsmentioning

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: Incompressible Flowsmentioning

confidence: 99%

HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB

Giacomini,

Sevilla,

Huerta

2020

Preprint

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This paper presentsHDGlab, 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 HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab 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 Gmsh is provided to facilitate its application to practical engineering problems.

show abstract

Arbitrary Lagrangian–Eulerian hybridizable discontinuous Galerkin methods for incompressible flow with moving boundaries and interfaces

Cited by 13 publications

References 61 publications

A conforming sliding mesh technique for an embedded‐hybridized discontinuous Galerkin discretization for fluid‐rigid body interaction

A conforming sliding mesh technique for an embedded‐hybridized discontinuous Galerkin discretization for fluid‐rigid body interaction

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

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