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Towards adaptive mesh refinement for the spectral element solver Nek5000
KTH, School of Engineering Sciences (SCI), Mechanics. (Linné flow centre)ORCID iD: 0000-0002-1724-0188
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-7448-3290
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2017 (English)Report (Refereed)
Abstract [en]

Hypre, a library for linear algebra, is used to replace a Matlab code for performing the setup step of an Algebraic Multigrid Method (AMG). The AMG method is used to compute part of the preconditioner in Nek5000, a code for Computational Fluid Dynamics based on the spectral element method. However, the solution of the AMG problem is not performed via Hypre but by Nek5000’s internal solver. The new AMG setup is shown to be faster by at least one order of magnitude, while it does not significantly impact the efficiency of the AMG solver, as is shown from its application to relevant test cases.

Place, publisher, year, edition, pages
2017. , p. 6
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-217497OAI: oai:DiVA.org:kth-217497DiVA, id: diva2:1156589
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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