The deal.II library, Version 9.0

Alzetta, Giovanni; Arndt, Daniel; Bangerth, Wolfgang; Boddu, Vishal; Brands, Benjamin; Davydov, Denis; Gassmöller, René; Heister, Timo; Heltai, Luca; Kormann, Katharina; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean Paul; Turcksin, Bruno; Wells, David

doi:10.1515/jnma-2018-0054

Cited by 177 publications

(155 citation statements)

References 29 publications

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“…At first, we want to compare the results obtained by the L 2 method (5) and the H(div) method (15) on the basis of the evolution of kinetic energy (u h ) = 1 2|Ω| ||u h || 2 L 2 and (negative) total kinetic energy dissipation rate − t (u h ) for the high-order choice k = 8; see also (23). In Figure 1 (top), both quantities are displayed on a sequence of meshes N ∈ {4, 8, 16}, which correspond to strongly underresolved, moderately resolved, and essentially resolved simulations.…”

Section: Comparison Of Methodsmentioning

confidence: 99%

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods

Fehn

Kronbichler

Lehrenfeld

et al. 2019

Numerical Methods in Fluids

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Summary The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the underresolved regime, mass conservation and energy stability are key ingredients to obtain robust and accurate discretisations. Recently, two approaches have been proposed in the context of high‐order discontinuous Galerkin (DG) discretisations that address these aspects differently. On the one hand, standard L2‐based DG discretisations enforce mass conservation and energy stability weakly by the use of additional stabilisation terms. On the other hand, pointwise divergence‐free H(div)‐conforming approaches ensure exact mass conservation and energy stability by the use of tailored finite element function spaces. This work raises the question whether and to which extent these two approaches are equivalent when applied to underresolved turbulent flows. This comparative study highlights similarities and differences of these two approaches. The numerical results emphasise that both discretisation strategies are promising for underresolved simulations of turbulent flows due to their inherent dissipation mechanisms.

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Section: Comparison Of Methodsmentioning

confidence: 99%

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods

Fehn

Kronbichler

Lehrenfeld

et al. 2019

Numerical Methods in Fluids

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“…In terms of the boundary layer thickness δ at the upper wall, the wall model extends up to approximately 10% to 20% of the boundary layer thickness for the lowest and medium Reynolds number and 5% to 12% at the highest Reynolds number. The mesh is mapped onto the exact hill geometry using the same polynomial ansatz as for the LES scale via manifold techniques available in the deal.II library . The enrichment degrees of freedom constitute equal or less than 0.1 % of the overall number of degrees of freedom.…”

Section: Numerical Examplesmentioning

confidence: 97%

“…The matrix forms are similar to the ones described in earlier studies . The numerical evaluation and integration is performed using the high‐performance sum factorization kernels by Kronbichler and Kormann available in the deal.II finite element library . Herein, the nonenriched cells are evaluated with Gaussian quadrature rules of appropriate order such that all integrals are evaluated exactly on affine cells ( k + 1 quadrature points for linear terms and

(⌊⌋, \frac{3 k}{2}) + 1

points for nonlinear terms).…”

Section: Application To a High‐order Dg Solvermentioning

confidence: 99%

A multiscale approach to hybrid RANS/LES wall modeling within a high‐order discontinuous Galerkin scheme using function enrichment

Krank

Kronbichler

Wall

2019

Numerical Methods in Fluids

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Summary We present a novel approach to hybrid Reynolds‐averaged Navier‐Stokes (RANS)/ large eddy simulation (LES) wall modeling based on function enrichment, which overcomes the common problem of the RANS‐LES transition and enables coarse meshes near the boundary. While the concept of function enrichment as an efficient discretization technique for turbulent boundary layers has been proposed in an earlier article by Krank & Wall (A new approach to wall modeling in LES of incompressible flow via function enrichment. J Comput Phys. 2016;316:94‐116), the contribution of this work is a rigorous derivation of a new multiscale turbulence modeling approach and a corresponding discontinuous Galerkin discretization scheme. In the near‐wall area, the Navier‐Stokes equations are explicitly solved for an LES and a RANS component in one single equation. This is done by providing the Galerkin method with an independent set of shape functions for each of these two methods; the standard high‐order polynomial basis resolves turbulent eddies, where the mesh is sufficiently fine and the enrichment automatically computes the ensemble‐averaged flow if the LES mesh is too coarse. As a result of the derivation, the RANS model is applied solely to the RANS degrees of freedom, which effectively prevents the typical issue of a log‐layer mismatch in attached boundary layers. As the full Navier‐Stokes equations are solved in the boundary layer, spatial refinement gradually yields wall‐resolved LES with exact boundary conditions. Numerical tests show the outstanding characteristics of the wall model regarding grid independence, superiority compared to equilibrium wall models in separated flows, and achieve a speed‐up by two orders of magnitude compared to wall‐resolved LES.

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“…1, consists of a flow in a two-dimensional channel with a length of 5 cm and a width of 2.5 cm. The flow is driven by the velocity profilev = (v 1 , 0) ,v 1 ≈ −11072.66x 2 + 348.79x 2 − 0.95 prescribed atx 1 = 0 m and the do-nothing boundary condition atx 1 = 0.025 m. The computations are performed using a timestep size of ∆t = 1 · 10 −3 s in an extension of the implementation [4] within the deal.II package [5]. The parameters in (5) are chosen asρ f = 1 g/cm 3 ,ν f = 3.5 · 10 −6 m/s 2 ,ρ s = 1.2 g/cm 3 , ν s = 0.48, E s = 4 · 10 5 N/m 2 , f f =f s = 0 N/m 3 andα u = 1 · 10 −8 .…”

Section: Numerical Examplementioning

confidence: 99%

A concept for aortic dissection with fluid‐structure‐crack interaction

Schussnig

Fries

2019

Proc Appl Math and Mech

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In aortic dissection, the layers composing the aorta rupture, allowing blood to enter the vessel wall. This process is modeled applying a monolithic fluid‐structure interaction framework, formulating the Navier‐Stokes equations for incompressible flows as well as the mixed finite strain elastodynamics equations in the Lagrangian frame of reference. Continuous test‐ and trial function spaces are employed in the whole domain, rendering the coupling straightforward. Within this contribution, a predefined function indicating failure is used to convert solid to fluid elements, thereby mimicing tissue rupture.

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The deal.II library, Version 9.0

Abstract: This paper provides an overview of the new features of the finite element library deal.II version 9.0.

Cited by 177 publications

References 29 publications

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods

A multiscale approach to hybrid RANS/LES wall modeling within a high‐order discontinuous Galerkin scheme using function enrichment

A concept for aortic dissection with fluid‐structure‐crack interaction

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The deal.II library, Version 9.0

Abstract: This paper provides an overview of the new features of the finite element library deal.II version 9.0.

Cited by 177 publications

References 29 publications

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L2 and H(div) methods

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L2 and H(div) methods

A multiscale approach to hybrid RANS/LES wall modeling within a high‐order discontinuous Galerkin scheme using function enrichment

A concept for aortic dissection with fluid‐structure‐crack interaction

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High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods

High‐order DG solvers for underresolved turbulent incompressible flows: A comparison of L² and H(div) methods