Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

Giorgiani, Giorgio; Fernández‐Méndez, Sonia; Huerta, Antonio

doi:10.1016/j.compfluid.2014.01.011

Cited by 58 publications

(80 citation statements)

References 51 publications

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“…Note that these Neumann boundary conditions do not correspond to regular stresses but to pseudo-stresses, as it is standard in velocity-pressure formulation, see [4]. However, more physical stress boundary conditions can also be implemented, see [7] for a detailed description.…”

Section: Navier-stokes Over a Broken Domainmentioning

confidence: 96%

“…A discussion on the choice of the stabilization parameter for a degree-adaptive HDG method applied to the Navier-Stokes equations can be found in [7]. A constant in the whole domain is suggested, with value kuk, where kuk is a characteristic velocity.…”

Section: The Hdg Local Problemmentioning

confidence: 99%

“…In this work, 2D vertical axis turbines are studied. On the one hand, a degree-adaptive Hybridizable Discontinuous Galerkin (HDG) method is used to solve this incompressible Navier-Stokes problem [3,7,8,15]. The HDG method allows to drastically reduce the coupled degrees of freedom (DOF) of the computation, seeking for an approximation of the solution that is defined only on the edges of the mesh.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Study of 2D Vertical Axis Wind and Tidal Turbines with a Degree-Adaptive Hybridizable Discontinuous Galerkin Method

Montlaur

Giorgiani

2015

Springer Tracts in Mechanical Engineering

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This work presents a 2D study of vertical axis turbines with application to wind or tidal energy production. On the one hand, a degree-adaptive Hybridizable Discontinuous Galerkin (HDG) method is used to solve this incompressible NavierStokes problem. The HDG method allows to drastically reduce the coupled degrees of freedom (DOF) of the computation, seeking for an approximation of the solution that is defined only on the edges of the mesh. The discontinuous character of the solution provides an optimal framework for a degree-adaptive technique. Degreeadaptivity further reduces the number of DOF in the HDG computation by means of degree-refining only where more precision is needed. On the other hand, the finite volume method of ANSYS ® is used to validate and compare the obtained results. IntroductionIn the last two decades, driven by the efforts to develop energy alternatives in order to reduce fossil fuel consumption and carbon emissions, wind power has been growing fast as an energy source, leading to cover 8 % of the European Union electricity consumption in 2013 [5]. Wind energy applications have first focused on locations where enhanced speed could be utilized to increase energy output, which explains why coastal and exposed hill tops have been preferred development sites, taking advantage of speed-up effects [2,13]. More recently, especially in the last 5 years, offshore renewable energy, including tidal and offshore wind energy, has been undergoing rapid development globally. 2013 was indeed a record year for offshore installations, with 1:567 MW of new capacity grid connected, and with A. Montlaur ( )

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Section: Navier-stokes Over a Broken Domainmentioning

confidence: 96%

Section: The Hdg Local Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Study of 2D Vertical Axis Wind and Tidal Turbines with a Degree-Adaptive Hybridizable Discontinuous Galerkin Method

Montlaur

Giorgiani

2015

Springer Tracts in Mechanical Engineering

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“…The only variable that can be affected by the splitting is the approximation of the trace along the interface in the case of Neumann boundary conditions, u i in (13). For simplicity, this variable can be approximated using a piecewise k-th order approximation, given by the k + 1 nodes defining the interface parametrization in each cut basic cell.…”

Section: Remarkmentioning

confidence: 99%

“…Therefore, a simple element-by-element postprocess of the derivatives leads to a superconvergent approximation of the primal vari-ables, with convergence of order k + 2inL 2 norm. The superconvergent solution can also be used to compute an efficient error estimator and define an adaptivity procedure [12,13].…”

Section: Introductionmentioning

confidence: 99%

eXtended Hybridizable Discontinous Galerkin (X-HDG) for Void Problems

et al. 2015

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A strategy for the Hybridizable Discontinous Galerkin (HDG) solution of problems with voids, inclusions or free surfaces is proposed. It is based on an eXtended Finite Element philosophy with a level-set description of interfaces. Thus, the computational mesh is not required to fit the interface (i.e. the boundary), simplifying and reducing the cost of mesh generation and, in particular, avoiding continuous remeshing for evolving interfaces. Differently to previous proposals for HDG solution with non-fitting meshes, here the computational mesh covers the domain, avoiding extrapolations, and ensuring the robustness of the method. The local problem at elements not cut by the interface, and the global problem, are discretized as usual in HDG. A modified local problem is considered at elements cut by the interface. At every cut element, an auxiliary trace variable on the boundary is introduced, which is eliminated afterwards using the boundary conditions on the interface, keeping the original unknowns and the structure of the local problem solver. An efficient and robust methodology for numerical integration in cut elements, in the context of high-order approximations, is also proposed. Numerical experiments demonstrate how X-HDG keeps the optimal convergence, superconvergence, and accuracy of HDG with no need of adapting the computational mesh to the interface boundary.

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Fluid description of neutral particles in divertor regimes in WEST

Valentinuzzi

Giorgiani

Marandet

et al. 2018

Contributions to Plasma Physics

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A new neutral fluid code has been developed as a necessary step towards a hybrid fluid/kinetic neutral model, to be used in ITER or DEMO simulations, where part of the divertor will be very collisional for neutrals. The neutral fluid code, which is able to handle complex geometries in view of the coupling to Soledge2D, is tested on plasma backgrounds obtained by Soledge2D‐Eirene in WEST geometry, for different divertor regimes, and is found to be in fair agreement with the kinetic Monte Carlo solver Eirene. The differences are due to the simplifications introduced in the fluid model and to the fact that a fluid description is not fully valid in these cases.

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Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier–Stokes equations

Cited by 58 publications

References 51 publications

Numerical Study of 2D Vertical Axis Wind and Tidal Turbines with a Degree-Adaptive Hybridizable Discontinuous Galerkin Method

Numerical Study of 2D Vertical Axis Wind and Tidal Turbines with a Degree-Adaptive Hybridizable Discontinuous Galerkin Method

eXtended Hybridizable Discontinous Galerkin (X-HDG) for Void Problems

Fluid description of neutral particles in divertor regimes in WEST

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