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Adjoint error estimators and adaptive mesh refinement in Nek5000
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-1724-0188
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-7448-3290
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
2017 (English)Report (Other academic)
Abstract [en]

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. In this report, we describe recent developments that have been made to enable adaptive mesh refinement in Nek5000 and we validate the method on simple, two-dimensional, steady test cases.We start by describing the modifications brought to Nek5000 that enable the presence of hanging nodes in the mesh. Thanks to this new feature, we can use the h-refinement technique for mesh adaptation, where selected elements are split via quadtree (2D) or octree (3D) structures. Then, two methods are considered to estimate and control the error. The first method is local and based on the spectral properties of the solution on each element. The second method is goal-oriented and takes into account both the local properties of the solution and the global dependence of the error in the solution via the resolution of an adjoint problem. Finally, the use of automatic mesh refinement is demonstrated in Nek5000 on two test cases: the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. Both error estimation methods are compared andare shown to efficiently reduce the number of degrees of freedom required to reach a given tolerance on the solution compared to conforming refinement. Moreover, the gains in terms of mesh generation, accuracy and computational cost are discussed by analysing the convergence of some functional of interest and the evolution of the mesh as refinement proceeds.

Place, publisher, year, edition, pages
2017.
Keywords [en]
Error estimators; mesh refinement; adaptivity; spectral element method
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-217498OAI: oai:DiVA.org:kth-217498DiVA, id: diva2:1156594
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20171123

Available from: 2017-11-13 Created: 2017-11-13 Last updated: 2017-11-23Bibliographically approved
In thesis
1. Towards adaptive mesh refinement in Nek5000
Open this publication in new window or tab >>Towards adaptive mesh refinement in Nek5000
2017 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. While such techniques have been known for a long time, most simulations do not make use of them because of the lack of a robust implementation. In this work, we present recent progresses that have been made to develop adaptive mesh refinement features in Nek5000, a code based on the spectral element method. These developments are driven by the algorithmic challenges posed by future exascale supercomputers. First, we perform the study of the strong scaling of Nek5000 on three petascale machines in order to assess the scalability of the code and identify the current bottlenecks. It is found that strong scaling limit ranges between 5, 000 and 220, 000 degrees of freedom per core depending on the machine and the case. The need for synchronized and low latency communication for efficient computational fluid dynamics simulation is also confirmed. Additionally, we present how Hypre, a library for linear algebra, is used to develop a new and efficient code for performing the setup step required prior to the use of an algebraic multigrid solver for preconditioning the pressure equation in Nek5000. Finally, the main objective of this work is to develop new methods for estimating the error on a numerical solution of the Navier–Stokes equations via the resolution of an adjoint problem. These new estimators are compared to existing ones, which are based on the decay of the spectral coefficients. Then, the estimators are combined with newly implemented capabilities in Nek5000 for automatic grid refinement and adaptive mesh adaptation is carried out. The applications considered so far are steady and two-dimensional, namely the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. The use of adaptive mesh refinement techniques makes mesh generation easier and it is shown that a similar accuracy as with a static mesh can be reached with a significant reduction in the number of degrees of freedom.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2017. p. 140
Series
TRITA-MEK, ISSN 0348-467X ; 2017:18
Keywords
Error estimators, mesh refinement, adaptivity, spectral element method, algebraic multigrid method
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-217501 (URN)978-91-7729-616-4 (ISBN)
Presentation
2017-12-11, E3, Kungliga Tekniska Högskolan, Osquars Backe 14, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Knut and Alice Wallenberg FoundationSwedish National Infrastructure for Computing (SNIC)EU, Horizon 2020, 671571
Note

QC 20171114

Available from: 2017-11-14 Created: 2017-11-13 Last updated: 2017-11-14Bibliographically approved

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