Versatile anisotropic mesh adaptation methodology applied to pure quantity of interest error estimator. Steady, laminar incompressible flow

Carrier, Alexandre; Deteix, Jean; Fortin, A.

doi:10.1002/fld.4790

Cited by 2 publications

(9 citation statements)

References 37 publications

(52 reference statements)

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“…The section extends the work done in a previous article 1 . We present some reminders but especially insist on additions and modifications linked to the turbulence, cubic hierarchic finite element field, and other improvements that allow handling highly anisotropic meshes.…”

Section: Adjoint Problem and Mesh Adaptationmentioning

confidence: 81%

“…Our upgraded version of the mesh adaptation methodology found in previous article 1 produces efficient and highly anisotropic meshes. Four modifications allow us to manage the anisotropic nature of the fields and the

ℙ^{2}

discretization.…”

Section: Discussionmentioning

confidence: 99%

“…Then, the general approach 1 allows us to obtain the following adjoint equations.

\begin{align} ℛ_{p_{*}} : & prefix- bold∇ \cdot {boldu}_{bold-italic*} = 0, \end{align}

\begin{align} {boldℛ}_{{boldu}_{bold-italic*}} : & prefix- boldu \cdot bold∇ {boldu}_{bold-italic*} + bold∇ boldu \cdot {boldu}_{bold-italic*} prefix- bold∇ p_{*} + k_{*} bold∇ k + ω_{*} bold∇ ω prefix- bold∇ \cdot (2 ν_{e} {bold∇}_{bolds} {boldu}_{bold-italic*}) = bold0, \end{align}

\begin{align} ℛ_{k_{*}} : & prefix- \frac{2}{3} bold∇ \cdot {boldu}_{bold-italic*} + \frac{2}{ω} {bold∇}_{bolds} {boldu}_{bold-italic*} : {bold∇}_{bolds} boldu prefix- boldu \cdot bold∇ k_{*} + β^{*} ω k_{*} prefix- bold∇ \cdot (ν_{k} bold∇ k_{*}) = 0, \end{align}

\begin{align} ℛ_{ω_{*}} : & prefix- \frac{4 k}{ω^{2}} \end{align}

…”

Section: Adjoint Problem and Mesh Adaptationunclassified

“…A promising methodology has been recently proposed and applied to steady laminar flow 1 . An error estimation based on adjoint sensitivity computation is used.…”

Section: Introductionmentioning

confidence: 99%

“…">1.We offer a new and practical implementation of Reynolds‐averaged Navier‐Stokes (RANS) equations with automatic wall treatment for velocity and turbulent variables for the finite element method. 2.We present improvements to the mesh adaptation methodology and the computation of the error estimation presented in reference work 1 …”

Section: Introductionmentioning

confidence: 99%

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Finite element implementation of k−ω SST with automatic wall treatment and adjoint‐based mesh adaptation

Carrier

2020

Numerical Methods in Fluids

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Summary This work presents a new methodology in finite element to simulate, according to a controlled precision on an engineering value, steady turbulent flows. First, we developed a new implementation of Reynolds‐averaged Navier‐Stokes equations combined with k−ω SST turbulence model and automatic wall treatment. Then, to simulate these complex multiscale flows, spatial discretization is critical. It is still common for expert users to generate meshes manually since they can roughly anticipate the physics of the flow. However, this remains a difficult task, especially for a neophyte. A recent mesh adaptation methodology based on an adjoint sensitivity analysis allows generating automatically appropriate meshes for analysis of steady laminar flows. Here, we extended this work to turbulent flows. The presentation is limited to two‐dimensional (2D) to demonstrate the effectiveness of the approach without getting unnecessarily entangled in the implementation details. The methodology is validated on the classic 2D zero pressure gradient flat plate verification case at Re = 5 · 106. Then, a more complex example is also presented: flow around multicomponent airfoil (30P30N, α=16.21∘) at Re = 9 · 106.

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Section: Adjoint Problem and Mesh Adaptationmentioning

confidence: 81%

ℙ^{2}

discretization.…”

Section: Discussionmentioning

confidence: 99%

“…Then, the general approach 1 allows us to obtain the following adjoint equations.

\begin{align} ℛ_{p_{*}} : & prefix- bold∇ \cdot {boldu}_{bold-italic*} = 0, \end{align}

\begin{align} {boldℛ}_{{boldu}_{bold-italic*}} : & prefix- boldu \cdot bold∇ {boldu}_{bold-italic*} + bold∇ boldu \cdot {boldu}_{bold-italic*} prefix- bold∇ p_{*} + k_{*} bold∇ k + ω_{*} bold∇ ω prefix- bold∇ \cdot (2 ν_{e} {bold∇}_{bolds} {boldu}_{bold-italic*}) = bold0, \end{align}

\begin{align} ℛ_{k_{*}} : & prefix- \frac{2}{3} bold∇ \cdot {boldu}_{bold-italic*} + \frac{2}{ω} {bold∇}_{bolds} {boldu}_{bold-italic*} : {bold∇}_{bolds} boldu prefix- boldu \cdot bold∇ k_{*} + β^{*} ω k_{*} prefix- bold∇ \cdot (ν_{k} bold∇ k_{*}) = 0, \end{align}

\begin{align} ℛ_{ω_{*}} : & prefix- \frac{4 k}{ω^{2}} \end{align}

…”

Section: Adjoint Problem and Mesh Adaptationunclassified

“…A promising methodology has been recently proposed and applied to steady laminar flow 1 . An error estimation based on adjoint sensitivity computation is used.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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