An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier–Stokes equations on moving domains

Horváth, Tamás L.; Rhebergen, Sander

doi:10.1016/j.jcp.2020.109577

Cited by 16 publications

(21 citation statements)

References 39 publications

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“…Besides classical approaches to steady and unsteady Navier-Stokes equations, HDG-based space-time formulations were studied for their ability to effectively handle moving and deforming domains. 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

Arch Computat Methods Eng

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“…Following [24,25] we consider a tetrahedral space-time mesh which is constructed as follows. First, the triangular spatial mesh of Ω n is extruded to the new time level t n+1 according to the domain deformation prescribed by the wave height.…”

Section: Space-time Notationmentioning

confidence: 99%

“…An exactly mass conserving space-time HDG discretization for the single-phase Navier-Stokes equations was introduced in [24,25]. Here we modify this discretization to take into account that the density and viscosity may be discontinuous across elements (see eq.…”

Section: Discretization Of the Momentum And Mass Equationsmentioning

confidence: 99%

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A Space-Time Hybridizable Discontinuous Galerkin Method for Linear Free-Surface Waves

Jones¹,

Lee²,

Rhebergen³

2020

J Sci Comput

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We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to identify the sharp interface between the two fluids. The incompressible two-fluid equations are discretized by an exactly mass conserving space-time hybridizable discontinuous Galerkin method while the level-set equation is discretized by a space-time embedded discontinuous Galerkin method. Different from alternative discontinuous Galerkin methods is that the embedded discontinuous Galerkin method results in a continuous approximation of the interface. This, in combination with the space-time framework, results in an interface-tracking method without resorting to smoothing techniques or additional mesh stabilization terms.

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“…Finally, we can see that these types of methods mentioned above has been applied to the incompressible Navier-Stokes equations [5,29]. In recent years, the space-time formulations of these types of methods have been developed for the incompressible Navier-Stokes equations on moving domains [4,9].…”

Section: Introductionmentioning

confidence: 99%

An embedded discontinuous Galerkin method for the Oseen equations

Han

Hou

2021

ESAIM: M2AN

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In this paper, the a prior error estimates of an embedded discontinuous Galerkin method for the Oseen equations are presented. It is proved that the velocity error in the L 2 (Ω) norm, has an optimal error bound with convergence order k + 1, where the constants are dependent on the Reynolds number (or ν − 1 ), in the diffusion-dominated regime, and in the convection-dominated regime, it has a Reynolds-robust error bound with quasi-optimal convergence order k +1 / 2. Here, k is the polynomial order of the velocity space. In addition, we also prove an optimal error estimate for the pressure. Finally, we carry out some numerical experiments to corroborate our analytical results.

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An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier–Stokes equations on moving domains

Cited by 16 publications

References 39 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

A Space-Time Hybridizable Discontinuous Galerkin Method for Linear Free-Surface Waves

An embedded discontinuous Galerkin method for the Oseen equations

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