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High Performance Adaptive Finite Element Methods: With Applications in Aerodynamics
KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).ORCID iD: 0000-0002-5020-1631
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The massive computational cost for resolving all scales in a turbulent flow makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized by adaptively resolution of the mesh, based on a posteriori error estimation. Such adaptive methods have previously been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations of turbulent flow for complex geometries with a posteriori error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph. We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than twelve thousands cores.

Abstract [sv]

Den höga beräkningskostnaden för att lösa upp alla turbulenta skalor för ett realistiskt problem gör en direkt numerisk simulering av Navier-Stokes ekvationer omöjlig. De senaste framstegen inom adaptiva finita element metoder ger ett nytt kraftfullt verktyg inom Computational Fluid Dynamics (CFD). Beräkningskostnaden för en simulering av turbulent flöde kan minimeras genom att beräkningsnätet adaptivt förfinas baserat på en a posteriori feluppskattning. Dessa adaptiva metoder har tidigare implementerats för seriella beräkningar, medan en effektiv parallellisering av metoden inte är trivial. I denna avhandling presenterar vi vår utveckling av en adaptiv finita element lösare, anpassad för att effektivt beräkna tidsupplösta approximationer i komplicerade geometrier med a posteriori felkontroll. Effektiva datastrukturer och metoder för ostrukturerade beräkningsnät av tetrahedrar presenteras. Avhandlingen behandlar även effektiv parallellisering av lokala nätförfiningsmetoder, exempelvis recursive longest edge bisection. Även lastbalanseringsproblematiken behandlas, där problemet lösts genom utvecklandet av en prediktiv dynamisk lastbalanseringsmetod, baserad på en viktad dualgraf av beräkningsnätet. Slutligen avhandlas även problematiken med att effektivt utnyttja nytillkomna superdatorarkitekturer, genom utvecklandet av en hybrid parallelliserings modell som kombinerar traditionell meddelande baserad parallellisering med envägskommunikation. Detta har resulterat i en generell samt effektiv implementation med god skalning upp till fler än tolv tusen processorkärnor.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xii, 50 p.
Series
TRITA-CSC-A, ISSN 1653-5723 ; 2013:07
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-125742ISBN: 978-91-7501-814-0 (print)OAI: oai:DiVA.org:kth-125742DiVA: diva2:640814
Public defence
2013-09-11, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20130816

Available from: 2013-08-16 Created: 2013-08-13 Last updated: 2016-02-02Bibliographically approved
List of papers
1. Framework For Massively Parallel Adaptive Finite Element Computational Fluid Dynamics On Tetrahedral Meshes
Open this publication in new window or tab >>Framework For Massively Parallel Adaptive Finite Element Computational Fluid Dynamics On Tetrahedral Meshes
2012 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 34, no 1, C24-C42 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we describe a general adaptive finite element framework for unstructured tetrahedral meshes without hanging nodes suitable for large scale parallel computations. Our framework is designed to scale linearly to several thousands of processors, using fully distributed and efficient algorithms. The key components of our implementation, local mesh refinement and load balancing algorithms, are described in detail. Finally, we present a theoretical and experimental performance study of our framework, used in a large scale computational fluid dynamics computation, and we compare scaling and complexity of different algorithms on different massively parallel architectures.

Keyword
adaptive methods, load balancing, unstructured local mesh refinement
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-30284 (URN)10.1137/100800683 (DOI)000300937500028 ()2-s2.0-84861384674 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20120326

Available from: 2011-02-21 Created: 2011-02-21 Last updated: 2013-08-16Bibliographically approved
2. A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions
Open this publication in new window or tab >>A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions
2011 (English)In: Quality And Reliability Of Large-Eddy Simulations II, Springer Netherlands, 2011, Vol. 16, no 1, 57-68 p.Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we present a computational study of turbulent flow separation for a circular cylinder at high Reynolds numbers. We use a stabilized finite element method together with skin friction boundary conditions, where we study flow separation with respect to the decrease of a friction parameter. In particular, we consider the case of zero friction corresponding to pure slip boundary conditions, for which we observe an inviscid separation mechanism of large scale streamwise vortices, identified in our earlier work. We compare our computational results to experiments for very high Reynolds numbers. In particular, we connect the pattern of streamwise vorticity in our computations to experimental findings of spanwise 3d cell structures reported in the literature.

Place, publisher, year, edition, pages
Springer Netherlands, 2011
Series
ERCOFTAC Series, ISSN 1382-4309 ; 16
Keyword
turbulent boundary layer, flow separation, General Galerkin method, a posteriori error estimation, adaptive finite element method, skin firction boundary conditions
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-30280 (URN)10.1007/978-94-007-0231-8_5 (DOI)000306194400005 ()2-s2.0-84964887723 (Scopus ID)978-94-007-0230-1 (ISBN)
Conference
2nd Workshop on Quality and Reliability of Large-Eddy Simulations, Univ Pisa, Pisa, Italy,Sep 09-11, 2009
Note

QC 20110224

Available from: 2011-02-21 Created: 2011-02-21 Last updated: 2013-12-13Bibliographically approved
3. Adaptive simulation of turbulent flow past a full car model
Open this publication in new window or tab >>Adaptive simulation of turbulent flow past a full car model
2011 (English)In: State of the Practice Reports, SC'11, 2011Conference paper, Published paper (Refereed)
Abstract [en]

The massive computational cost for resolving all turbulent scales makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. We present recent advances in parallel adaptive finite element methodology that enable us to efficiently compute time resolved approximations for complex geometries with error control. In this paper we present a LES simulation of turbulent flow past a full car model, where we adaptively refine the unstructured mesh to minimize the error in drag prediction. The simulation was partly carried out on the new Cray XE6 at PDC/KTH where the solver shows near optimal strong and weak scaling for the entire adaptive process.

National Category
Computer and Information Science
Identifiers
urn:nbn:se:kth:diva-58720 (URN)10.1145/2063348.2063375 (DOI)2-s2.0-83055188819 (Scopus ID)978-145031139-7 (ISBN)
Conference
ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis SC'11
Note
QC 20120202Available from: 2012-01-08 Created: 2012-01-08 Last updated: 2013-08-16Bibliographically approved
4. Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry
Open this publication in new window or tab >>Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry
Show others...
2013 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 80, no SI, 310-319 p.Article in journal (Refereed) Published
Abstract [en]

We present a framework for adaptive finite element computation of turbulent flow and fluid structure interaction, with focus on general algorithms that allow for complex geometry and deforming domains. We give basic models and finite element discretization methods, adaptive algorithms and strategies for efficient parallel implementation. To illustrate the capabilities of the computational framework, we show a number of application examples from aerodynamics, aero-acoustics, biomedicine and geophysics. The computational tools are free to download open source as Unicorn, and as a high performance branch of the finite element problem solving environment DOLFIN, both part of the FEniCS project.

Keyword
Unicorn, DOLFIN, FEniCS, Parallel adaptive finite element method, Open source software, Turbulent flow, Fluid structure interaction, Complex geometry, Deforming domain
National Category
Computer and Information Science
Identifiers
urn:nbn:se:kth:diva-124954 (URN)10.1016/j.compfluid.2012.02.003 (DOI)000320427200036 ()2-s2.0-84885190916 (Scopus ID)
Funder
EU, European Research CouncilSwedish Foundation for Strategic Research Swedish Research CouncilSwedish Energy Agency
Note

QC 20130803

Available from: 2013-08-02 Created: 2013-08-02 Last updated: 2017-12-06Bibliographically approved
5. Optimizing Sparse Matrix Assembly in Finite Element Solvers with One-Sided Communication
Open this publication in new window or tab >>Optimizing Sparse Matrix Assembly in Finite Element Solvers with One-Sided Communication
2013 (English)In: High Performance Computing for Computational Science - VECPAR 2012, Springer Berlin/Heidelberg, 2013, 128-139 p.Conference paper, Published paper (Refereed)
Abstract [en]

In parallel finite element solvers, sparse matrix assembly is often a bottleneck. Implemented using message passing, latency from message matching starts to limit performance as the number of cores increases. We here address this issue by using our own stack based representation of the sparse matrix, and a hybrid parallel programming model combining traditional message passing with one-sided communication. This gives an significantly faster insertion rate compared to state of the art implementations on a Cray XE6.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2013
Series
Lecture Notes in Computer Science, ISSN 0302-9743 ; 7851
Keyword
UPC, PGAS, Hybrid Parallel Programming
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-125739 (URN)10.1007/978-3-642-38718-0_15 (DOI)000342997100015 ()2-s2.0-84883275982 (Scopus ID)978-3-642-38717-3 (ISBN)
Conference
10th International Conference on High Performance Computing for Computational Science, VECPAR 2012; Kobe; Japan; 17 July 2012 through 20 July 2012
Note

QC 20130815

Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2014-11-13Bibliographically approved
6. Towards a Parallel Algebraic Multigrid Solver Using Partitioned Global Address Space
Open this publication in new window or tab >>Towards a Parallel Algebraic Multigrid Solver Using Partitioned Global Address Space
2013 (English)Report (Other academic)
Abstract [en]

The Algebraic Multigrid (AMG) method has over the years developed into an ecient tool for solving unstructured linear systems. The need to solve large industrial problems discretized on unstructured meshes, has been a key motivation for devising a parallel AMG method. Despite some success, the key part of the AMG algorithm; the coarsening step, is far from trivial to parallelize eciently. We here introduce a novel parallelization of the Ruge-Stüben coarsening algorithm, that retains the good interpolation properties of the original method. Our parallelization is based on the Partitioned Global Address Space (PGAS) abstraction, which allows for a simple, yet efficient implementation. The solver is described in detail and a performance study on a Cray XE6 is presented.

Publisher
15 p.
Series
CTL Technical Report, 30
Keyword
Algebraic Multigrid, PGAS, UPC
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-125620 (URN)
Note

QC 20130815

Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2013-08-16Bibliographically approved
7. Improving Parallel Performance of FEniCS Finite Element Computations by Hybrid MPI/PGAS
Open this publication in new window or tab >>Improving Parallel Performance of FEniCS Finite Element Computations by Hybrid MPI/PGAS
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present our work on developing a hybrid parallel programming model for a general finite element solver. The main focus of our work is to demonstrate that legacy codes with high latency, two-sided communication in the form of message passing can be improved using lightweight one-sided communication. We introduce a new hybrid MPI/PGAS implementation of the open source general finite element framework FEniCS, replacing the linear algebra backend (PETSc) with a new library written in UPC. A detailed description of the linear algebra backend implementation and the hybrid interface to FEniCS is given. We also present a detailed analysis of the performance of this hybrid solver on the Cray XE6 Lindgren at PDC/KTH including a comparison with the MPI only implementation, where we find that the hybrid implementation results in significant improvements in performance of the solver.

National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:kth:diva-125617 (URN)
Note

QS 2013

Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2013-08-16Bibliographically approved
8. Adaptive Computation of Aeroacoustic Sources for a Rudimentary Landing Gear
Open this publication in new window or tab >>Adaptive Computation of Aeroacoustic Sources for a Rudimentary Landing Gear
2014 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 74, no 6, 406-421 p.Article in journal (Refereed) Published
Abstract [en]

We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall-layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations.

Keyword
aeroacoustics, aerodynamics, finite element, incompressible flow, LES, large Eddy simulations;turbulent flow
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-125722 (URN)10.1002/fld.3856 (DOI)000329509500002 ()2-s2.0-84891832461 (Scopus ID)
Funder
Swedish Foundation for Strategic Research EU, European Research CouncilSwedish Research CouncilSwedish Energy Agency
Note

QC 20140131

Available from: 2013-08-13 Created: 2013-08-13 Last updated: 2017-12-06Bibliographically approved
9. Computation of aeroacoustic sources for a Gulfstream G550 nose landing gear model using adaptive FEM
Open this publication in new window or tab >>Computation of aeroacoustic sources for a Gulfstream G550 nose landing gear model using adaptive FEM
2016 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 124, 136-146 p.Article in journal (Refereed) Published
Abstract [en]

This work presents a direct comparison of unsteady, turbulent flow simulations with measurements performed using a Gulfstream G550 nose landing gear model. The experimental campaign, which was carried out by researchers from the NASA Langley Research Center, provided a series of detailed, well documented wind-tunnel measurements for comparison and validation of computational fluid dynamics (CFD) and computational aeroacoustics (CAA) methodologies. Several computational efforts were collected and presented at the Benchmark for Airframe Noise Computation workshops, BANC-I and II. For our simulations, we used a General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh is adaptively refined with respect to a posteriori estimates of the error in a quantity of interest, here the source term in Lighthill's equation. The mesh is fully unstructured and the solution is time-resolved, which are key ingredients for solving problems of industrial relevance in the field of aeroacoustics. Moreover, we choose to model the boundary layers on the landing gear geometry with a free-slip condition for the velocity, which we previously observed to produce good results for external flows at high Reynolds numbers, and which considerably reduces the amount of cells required in the mesh. The comparisons presented here are an attempt to quantify the accuracy of our models, methods and assumptions; to that end, several results containing both time-averaged and unsteady flow quantities, always side by side with corresponding experimental values, are reported. The main finding is that we are able to simulate a complex, unsteady flow problem using a parameter-free methodology developed for high Reynolds numbers, external aerodynamics and aeroacoustics applications.

Place, publisher, year, edition, pages
Elsevier, 2016
Keyword
Landing gear noise, Computational fluid dynamics, Computational aeroacoustics, Adaptive finite element methods, Turbulence, CAA, CFD, FEM
National Category
Computer Science
Identifiers
urn:nbn:se:kth:diva-180964 (URN)10.1016/j.compfluid.2015.10.017 (DOI)000367282700011 ()2-s2.0-84946867009 (Scopus ID)
Note

Updated from Manuscript to Article.

QC 20160128

Available from: 2016-01-28 Created: 2016-01-26 Last updated: 2017-11-30Bibliographically approved

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Jansson, Niclas

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
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