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Performance Analysis of the LU-SGS Algorithm as Multigrid Smoother in a CFD Code for Unstructured Grids
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Aerodynamics.ORCID iD: 0000-0001-9902-6216
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Lower-Upper Symmetric Gauss-Seidel (LU-SGS) approximate solution forlinear systems has been implemented in the CFD codeEdge, an edge-based Navier-Stokes flow solver for unstructured grids,in order to accelerate the convergence to steady state.LU-SGS has been combined with the line-implicit technique to improve convergenceon the very anisotropic grids necessary for typical High Reynolds number applications, giving theline LU-SGS.The performance of the LU-SGS algorithm is analyzed for a better comprehension ofthe solver behavior and capabilities, and to obtain maximal efficiency for2D and 3D, Euler and Reynolds-Averaged Navier-Stokes computations.The study covers code implementation using performance analysis tools, andnumerical techniques such as node ordering methods, and parallelization.The results show that by code tuning, the wall clock time was reduced by a factor of two.The node ordering influences the convergence, and orderingscoming from different types of mesh generators were close to optimal. The LU-SGS algorithm was successfully parallelized by domain decompositionand run for cases up to 110M grid points, showing linear scaling withnumber of processors. The tests indicate that 10 LU-SGS iterations is a requirementfor minimal computing time on large grids, and that multigrid acceleration may be ineffective.The computing time with line LU-SGS was about half that of theline-implicit Runge-Kutta solver for 3D Reynolds-Averaged Navier-Stokes.

Keyword [en]
CFD convergence acceleration; LU-SGS; line-implicit; parallelization; ordering techniques; multigrid
National Category
Aerospace Engineering
Identifiers
URN: urn:nbn:se:kth:diva-156413OAI: oai:DiVA.org:kth-156413DiVA: diva2:766626
Note

QS 2014

Available from: 2014-11-27 Created: 2014-11-27 Last updated: 2014-12-01Bibliographically approved
In thesis
1. Acceleration of Compressible Flow Simulations with Edge Using  Implicit Time Stepping
Open this publication in new window or tab >>Acceleration of Compressible Flow Simulations with Edge Using  Implicit Time Stepping
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Computational fluid dynamics (CFD) is a significant tool routinely used indesign and optimization in aerospace industry. Often cases with unsteadyflows must be computed, and the long compute times of standard methods hasmotivated the present work on new implicit methods to replace the standardexplicit schemes. The implementation and numerical experiments were donewith the Swedish national flow solver Edge, developed by FOI,universities, and collaboration partners.The work is concentrated on a Lower-Upper Symmetric Gauss-Seidel (LU-SGS)type of time stepping. For the very anisotropic grids needed forReynolds-Averaged Navier-Stokes (RANS) computations of turbulent boundary layers,LU-SGS is combined with a line-implicit technique.  The inviscid flux Jacobians which contribute to the diagonalblocks of the system matrix are based on a flux splitting method with upwind type dissipation giving  control over diagonal dominance and artificial dissipation.The method is  controlled by several parameters, and comprehensivenumerical experiments were carried out to identify their influence andinteraction so that close to optimal values can be suggested. As an example,the optimal number of iterations carried out in a time-step increases with increased resolution of the computational grid.The numbering of the unknowns is important, and the numberings produced by mesh generators of Delaunay- and advancing front-type wereamong the best.The solver has been parallelized with the Message Passing Interface (MPI) for runs on multi-processor hardware,and its performance scales with the number of processors at least asefficiently as the explicit methods. The new method saves typicallybetween 50 and 80 percent of the runtime, depending on the case, andthe largest computations have reached 110M grid nodes. Theclassical multigrid acceleration for 3D RANS simulations was foundineffective in the cases tested in combination with the LU-SGS solverusing optimal parameters. Finally, preliminary time-accurate simulations for unsteady flows have shown promising results.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. xv, 97 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2014:72
Keyword
Compressible CFD, Convergence Acceleration, Implicit Time-Stepping, LU-SGS, Upwind Type Dissipation, Line-implicit, Ordering, Parallelization, Parameters, Multigrid
National Category
Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-156414 (URN)978-91-7595-370-0 (ISBN)
Public defence
2014-12-12, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Note

QC 20141201

Available from: 2014-12-01 Created: 2014-11-27 Last updated: 2014-12-01Bibliographically approved

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Otero, Evelyn

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