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Acceleration of Compressible Flow Simulations with Edge Using  Implicit Time Stepping
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Aerodynamics.ORCID iD: 0000-0001-9902-6216
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 [en]
Compressible CFD, Convergence Acceleration, Implicit Time-Stepping, LU-SGS, Upwind Type Dissipation, Line-implicit, Ordering, Parallelization, Parameters, Multigrid
National Category
Aerospace Engineering
Identifiers
URN: urn:nbn:se:kth:diva-156414ISBN: 978-91-7595-370-0 (print)OAI: oai:DiVA.org:kth-156414DiVA: diva2:766643
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
List of papers
1. Convergence Acceleration of the CFD Code Edge by LU-SGS
Open this publication in new window or tab >>Convergence Acceleration of the CFD Code Edge by LU-SGS
2011 (English)In: 3rd CEAS European Air & Space Conference, Venice, 24-28 October 2011, CEAS/AIDAA , 2011, 606-611 p.Conference paper, Published paper (Refereed)
Abstract [en]

Edge is a flow solver for unstructured grids based on a dual grid and edge-based formulation. The standard dual-time stepping methods for compressible unsteady flows are inadequate for large-scale industrial problems. This has motivated the present work, in which an implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) type of relaxation has been implemented in the code Edge with multigrid acceleration. Two different types of dissipation, a scalar and a matrix model, have been constructed which increase the diagonal dominance of the system matrix but not the numerical viscosity of the computed solution. A parametric study demonstrates convergence accelerations by a factor of three for inviscid transonic flows compared to explicit Runge-Kutta smoothing for multigrid acceleration.

Place, publisher, year, edition, pages
CEAS/AIDAA, 2011
Keyword
compressible CFD, convergence acceleration, implicit time-stepping, matrix dissipation
National Category
Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-78943 (URN)
Conference
3rd CEAS European Air & Space Conference
Note
QC 20120209Available from: 2012-02-09 Created: 2012-02-08 Last updated: 2014-12-01Bibliographically approved
2. Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation
Open this publication in new window or tab >>Acceleration on stretched meshes with line-implicit LU-SGS in parallel implementation
2015 (English)In: International journal of computational fluid dynamics (Print), ISSN 1061-8562, E-ISSN 1029-0257, Vol. 29, no 2, 133-149 p.Article in journal (Refereed) Published
Abstract [en]

The implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver is combined with the line-implicit technique to improve convergence on the very anisotropic grids necessary for resolving the boundary layers. The computational fluid dynamics code used is Edge, a Navier-Stokes flow solver for unstructured grids based on a dual grid and edge-based formulation. Multigrid acceleration is applied with the intention to accelerate the convergence to steady state. LU-SGS works in parallel and gives better linear scaling with respect to the number of processors, than the explicit scheme. The ordering techniques investigated have shown that node numbering does influence the convergence and that the orderings from Delaunay and advancing front generation were among the best tested. 2D Reynolds-averaged Navier-Stokes computations have clearly shown the strong efficiency of our novel approach line-implicit LU-SGS which is four times faster than implicit LU-SGS and line-implicit Runge-Kutta. Implicit LU-SGS for Euler and line-implicit LU-SGS for Reynolds-averaged Navier-Stokes are at least twice faster than explicit and line-implicit Runge-Kutta, respectively, for 2D and 3D cases. For 3D Reynolds-averaged Navier-Stokes, multigrid did not accelerate the convergence and therefore may not be needed.

Keyword
line-implicit, convergence acceleration, line-implicit LU-SGS, implicit time-stepping, parallelisation, LU-SGS, ordering techniques
National Category
Aerospace Engineering
Research subject
Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-156412 (URN)10.1080/10618562.2015.1021692 (DOI)000352611900001 ()2-s2.0-84927796786 (Scopus ID)
Note

QC 20141201. Updated from accepted to published.

Available from: 2014-11-27 Created: 2014-11-27 Last updated: 2017-12-05Bibliographically approved
3. Parameter Investigation with Line-Implicit Lower-Upper Symmetric Gauss-Seidel on 3D Stretched Grids
Open this publication in new window or tab >>Parameter Investigation with Line-Implicit Lower-Upper Symmetric Gauss-Seidel on 3D Stretched Grids
2014 (English)Conference paper, Published paper (Refereed)
Abstract [en]

An implicit Lower-Upper Symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit methodas an acceleration technique for Reynolds-Averaged Navier-Stokes (RANS) simulation on stretched meshes.The Computational Fluid Dynamics code concerned is Edge, an edge-based finite volume Navier-Stokesflow solver for structured and unstructured grids.The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGSsolver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the Left Hand Side dissipation,and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme.The influence of these parameters on the overall convergence is presented and default values are defined formaximum convergence acceleration. The optimized settings are applied to 3D RANScomputations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

National Category
Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-156411 (URN)
Conference
AIAA AVIATION 2014 - 44th AIAA Fluid Dynamics Conference
Note

QC 20141201

Available from: 2014-11-27 Created: 2014-11-27 Last updated: 2014-12-01Bibliographically approved
4. Performance Analysis of the LU-SGS Algorithm as Multigrid Smoother in a CFD Code for Unstructured Grids
Open this publication in new window or tab >>Performance Analysis of the LU-SGS Algorithm as Multigrid Smoother in a CFD Code for Unstructured Grids
(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
CFD convergence acceleration; LU-SGS; line-implicit; parallelization; ordering techniques; multigrid
National Category
Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-156413 (URN)
Note

QS 2014

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

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