International Workshop on High-Order CFD Methods
International collaboration providing enhanced understanding of the most current and developing needs for CFD researchers and managers.
This webpage contains information on the Third Workshop on High-Order CFD Methods as well as three subsequent AIAA invited sessions on related topics.
The International Workshops on High-Order CFD Methods were held alternately between USA and EU: first 2012, second 2013, third 2015, fourth 2016, and fifth 2019.
The workshops provide an open and impartial forum for evaluating the status of high-order methods (order of accuracy > 2) in solving a wide range of fluid flow problems.
International collaboration at the conference provides enhanced understanding of the most current and developing needs for CFD researchers and managers in academia, government and industry.
This webpage contains information on the 2015 workshop as well as three subsequent AIAA invited sessions on related topics. If you have any questions, please contact hung.t.huynh@nasa.gov.
Presentations
AIAA-AVIATION 2017 Special Session
CFD-15. Capabilities and Challenges in CFD I: Academia, Government, and Industry Perspectives
Chaired by: H.T. HUYNH, NASA Glenn Research Center and E. JOHNSEN, University of Michigan
- Presentation of Dimitri Mavriplis (University of Wyoming)
- Presentation of Michael Rogers (NASA)
- Presentation of David McDaniel (DoD)
- Presentation of Steve Karman (Pointwise)
- Presentation of Antony Jameson (Stanford University)
CFD-19. Towards Industrial LES and DNS for Aeronautics
Chaired by: H.T. HUYNH, NASA Glenn Research Center and C. HIRSCH, Numeca, International S. A.
- Presentation of Charles Hirsch (NUMECA)
- Presentation of Andrey Wolkov (TsAGI)
- Presentation of Aravind Balan (CERFACS)
- Presentation of William Dawes (Cambridge Flow Solutions)
AIAA-SciTech 2015 Invited Sessions
Current Challenges for Computational Fluid Dynamics, Industry and Government Interest I and II
Chaired by: H.T. HUYNH, NASA Glenn Research Center and N. KROLL, DLR – German Aerospace Center
- Presentation of John Vassberg (Boeing)
- Presentation of Robert Bush (Pratt & Whitney)
- Presentation of Brian Smith (Lockheed Martin)
- Presentation of Antony Jameson (Stanford University)
- Presentation of Vincent Couaillier (ONERA)
- Presentation of Norbert Kroll (DLR)
- Presentation of Charles Hirsch (NUMECA)
Workshop Details
Final Agenda
Download the final agenda for the workshop here.
Objectives
- To provide an open and impartial forum for evaluating the status of high-order methods (order of accuracy > 2) in solving a wide range of flow problems.
- To assess the performance of high-order methods through comparison to production 2nd order CFD codes widely used in the aerospace industry with well defined metrics.
- To identify pacing items in high-order methods needing additional research and development in order to proliferate in the CFD community.
- To facilitate international collaboration and enhance mutual understanding among CFD researchers and managers in academia, government, and industries.
General Information
- The workshop is open to participants all over the world. Everybody is welcome.
- Several benchmark cases are included for the workshop. To be considered as speakers, participants should complete as least one sub-case.
- Open forums will be included in the workshop to discuss pacing items and further research areas in high-order methods.
- A number of fellowships will be provided by Army Research Office (ARO) and NASA to pay registration fees for graduate and undergraduate students to attend the workshop and present their work. E-mail hung.t.huynh@nasa.gov if you would like to apply.
Important Dates
- June 15, 2014 – Test cases defined with most geometries available. (New Date)
- June 30, 2014 – E-mail hung.t.huynh@nasa.gov for your intention to participate (for general planning purposes only).
- October 15, 2014 – Abstract deadline (abstract template). Send an (incomplete) abstract if you believe data will be ready on November 15, 2014.
- November 1, 2014 – Acceptance e-mail sent out.
- November 15, 2014 November 30, 2014 – Submit both results and (revised) abstract (pdf) for each problem to the problem lead(s) email address(es) and hung.t.huynh@nasa.gov.
- January 3-4, 2015 – Workshop
Important Guidelines (Read this first!)
Notes for all participants. If you have general questions, send an e-mail to: hung.t.huynh@nasa.gov.
Questions on specific test problems can be sent directly to the person(s) in charge of the problem.
Venue and Accommodation
The workshop will take place January 3-4, 2015 just before the 53rd AIAA Aerospace Sciences Meeting at the Gaylord Palms Resort and Convention Center in Kissimmee, Florida (Orlando).
Test Cases
Several benchmark cases from the 1st and 2nd International Workshops on High-Order CFD Methods are included.
New problems are being added and will be available by April 30, 2014.
NOTICE TO PARTICIPANTS
The number of test cases has been consolidated for the third workshop.
Therefore the numbers assigned to each test case will NOT necessarily match those of the previous workshops.
C1. Easy, 2D
C1.1
PDF Download | Contact | Images |
Transonic Ringleb flow | hung.t.huynh@nasa.gov | p4 quad grids (8/25/11) |
C1.2
PDF Download | Contact | Images |
Flow over the NACA0012 airfoil, inviscid and viscous, subsonic and transonic | May, may@aices.rwth-aachen.de | p4 quad & triangular grids (far field boundary over 1000 chords away) (1/14/13) |
C1.3
PDF Download | Contact | Images |
Flat plate boundary layer | Bassi, francesco.bassi@unibg.it and Darmofal, darmofal@mit.edu (1/30/11) | quad grids (9/23/11) (being modified to include turbulent flows) |
C1.4
PDF Download | Contact | Images |
Vortex transport by uniform flow | doru.caraeni@us.cd-adapco.com (Updated on 10/05/11) | Grids (4/11/11) |
C2. Intermediate, 2D & 3D
C2.1
PDF Download | Contact | Images |
Turbulent flow over a RAE airfoil | Deconinck, deconinck@vki.ac.be | Linear and higher order grids (1/14/13) |
C2.2
PDF Download | Contact | Images |
Delta wing at low Reynolds number | Hartmann, Ralf.Hartmann@dlr.de | Grids (updated 8/15/11) |
C2.3
PDF Download | Contact | Images |
Heaving and Pitching Airfoil | Persson, persson@berkeley.edu Fidkowski, kfid@umich.edu, (updated 5/23/14) |
C3. Difficult, 2D & 3D
C3.1
PDF Download | Contact | Images |
Turbulent flow over a multi-element airfoil | Marco Ceze, mceze@umich.edu (1/30/11) | Geometry and Grids (10/17/2014) |
C3.2
PDF Download | Contact | Images |
Turbulent flow over DPW III wing alone | Fidkowski, kfid@umich.edu (1/30/11) | Grids (6/5/2014) |
C3.3
PDF Download | Contact | Images |
Direct Numerical Simulation of the Taylor-Green Vortex at Re = 1600 | Hillewaert, koen.hillewaert@cenaero.be (4/18/11) |
Reference Data (8/24/11) |
C3.4
PDF Download | Contact | Images |
DNS and LES of flow over 2D periodic hill | Carton de Wiart, corentin.carton@cenaero.be | Linear and High-Order Grids (1/29/13) |
C3.5
PDF Download | Contact | Images |
CRM wing/body | Leicht, tobias.leicht@dlr.de (2/6/13 | grids (2/6/13) |
C3.6
PDF Download | Contact | Images |
Shock Wave/Boundary Layer Interaction (SWBLI) | Couaillier, vincent.couaillier@onera.fr (9/2/14) | grids and reference data to be added |
Workshop Results
C1. Easy, 2D
C1.1 Transonic Ringleb flow – Summary by H.T. Huynh
- Chris Fidkowski (Michigan)
- David Friedlander (NASA Glenn)
- Giorgio Giangaspero, Edwin van der Weide, Magnus Svärd, Mark H. Carpenter, and Ken Mattson (Twente)
- Jean-Marie Le Gouez (ONERA)
- Antonio Garcia-Uceda and Charles Hirsch (NUMECA)
C1.2 Flow over the NACA0012 airfoil – Summary by G. May
- Aravind Balan, Georg May, and Michael Woopen (Aachen)
- Shun Zhang and Chris Fidkowski (Michigan) – Hanging-Node Adaptive Refinement
- Shun Zhang and Chris Fidkowski (Michigan) – Anisotropic Metric-Based Refinement (using BAMG)
- Giorgio Giangaspero, Edwin van der Weide, Magnus Svärd, Mark H. Carpenter, and Ken Mattson (Twente)
- Takanori Haga, Seiji Tsutsumi, Ryoji Takaki, and Eiji Shima (JAXA)
- Nicolas Ringue, Brian Vermeire, and Siva Nadarajah (McGill)
- Andrea Ferrero and Francesco Larocca (Torino)
- Peter Eliasson, Jan Nordström,and Marco Kupiainen (FOI – Swedish Def.R.A.)
- Lei Shi and Z. J. Wang (Kansas)
- Antonio Garcia-Uceda and Charles Hirsch (NUMECA)
C1.3 Flat plate boundary layer – Summary by M. Galbraith and D. Darmofal
- Farshad Navah, Brian Vermeire, and Siva Nadarajah (McGill)
- Johann Dahm and Chris Fidkowski (Michigan)
- Michael Woopen, Aravind Balan, and Georg May (Aachen)
- Andrea Ferrero and Francesco Larocca (Torino)
- Lei Shi and Z. J. Wang (Kansas)
C1.4 Vortex transport by uniform flow – Summary by D. Caraeni
- David Friedlander (NASA Glenn)
- Philip Zwanenburg, Brian Vermeire and Siva Nadarajah (McGill)
- Shun Zhang and Chris Fidkowski (Michigan)
- Giorgio Giangaspero, Edwin van der Weide, Magnus Svärd, Mark H. Carpenter, and Ken Mattson (Twente)
- Florent Renac and Raphaël Blanchard (ONERA)
C2. Intermediate, 2D & 3D
C2.1 Turbulent flow over a RAE airfoil – Summary by K. Fidkowski
- Giorgio Giangaspero, Edwin van der Weide, Magnus Svärd, Mark H. Carpenter, and Ken Mattson (Twente)
- Johann Dahm and Chris Fidkowski (Michigan)
C2.2 Delta wing at low Reynolds number – Summary by R. Hartmann
- Chris Fidkowski (Michigan)
- Xiaodong Liu, Yidong Xia, and Hong Luo (NC State)
- Michael Woopen, Aravind Balan, and Georg May (Aachen)
C2.3 Heaving and Pitching Airfoil – Summary by P. Persson
- Daniel J. Garmann and Miguel R. Visbal (AFRL)
- Jean-Marie Le Gouez (ONERA)
- Michael Wurst, Manuel Kessler, and Ewald Krämer (Stuttgart)
- Alejandro A. Figueroa, German Weht, Carlos G. Sacco, and Shing Chan Chang (Argentina)
- Caleb Yow, Bin Zhang, and Chunlei Liang (George Washington)
- Chris Fidkowski (Michigan)
- Per-Olof Persson (Berkeley)
C3. Difficult, 2D & 3D
C3.1 Turbulent flow over a multi-element airfoil – Summary by M. Ceze
- Marco Ceze and Chris Fidkowski (Michigan)
- Marcel Wallraff and Tobias Leicht (DLR) and Presentation
- Michael Wurst, Manuel Kessler, and Ewald Krämer (Stuttgart)
- A.F. Antoniadis, P. Tsoutsanis, D. Drikakis (Cranfield)
C3.2 Turbulent flow over DPW III wing – Summary by M. Ceze
- Marco Ceze and Chris Fidkowski (Michigan)
- Michael Brazell and Dimitri J. Mavriplis (Wyoming) and Presentation
C3.3 Direct Numerical Simulation of the Taylor-Green Vortex – Summary by K. Hillewaert
- Laslo Diosady and Scott M. Murman (NASA Ames)
- A. Mastellone, Francesco Capuano, S. Di Benedetto, and L. Cutrone (CIRA)
- Brian Vermeire, Freddie Witherden, and Peter Vincent (Imperial College London)
- Xiaodong Liu, Yidong Xia, and Hong Luo (NC State)
- Giorgio Giangaspero, Edwin van der Weide, Magnus Svärd, Mark H. Carpenter, and Ken Mattson (Twente)
- Michael Brazell and Dimitri J. Mavriplis (Wyoming) and Presentation
- Philip Zwanenburg, Brian Vermeire and Siva Nadarajah (McGill)
- Andrea D. Beck, David Flad, Thomas Bolemann, Claus-Dieter Munz (Stuttgart)
- Daniel J. Garmann and Miguel R. Visbal (AFRL)
C3.4 DNS and LES of flow over 2D periodic hill – Summary by C.C. de Wiart
- Laslo Diosady and Scott M. Murman (NASA Ames)
- Marta de la Llave Plata and Vincent Couaillier (ONERA)
- Daniel J. Garmann and Miguel R. Visbal (AFRL)
- Corentin Carton de Wiart, Koen Hillewaert (Cenaero)
- Jonathan Bull and Antony Jameson (Stanford)
- Thomas Bolemann, Andrea Beck, Claus-Dieter Munz (Stuttgart)
- A.F. Antoniadis, Z. Rana, P. Tsoutsanis, D. Drikakis (Cranfield)
C3.5 CRM wing/body – Summary by T. Leicht
- Marco Ceze and Chris Fidkowski (Michigan)
- Ralf Hartmann (DLR)
C3.6 Shock Wave/Boundary Layer Interaction – Summary by V. Couaillier
- Florent Renac and Vincent Couaillier (ONERA)
Organizing Committee
- H.T. Huynh (Co-Chair, Local Organizer), NASA Glenn Research Center
- Norbert Kroll(Co-Chair), DLR
- Z.J. Wang (Chair-Emeritus), University of Kansas
- Remi Abgrall, University of Zurich
- Francesco Bassi, University of Bergamo
- Doru Caraeni, CD-adapco
- Mark H. Carpenter, NASA Langley Research Center
- Corentin Carton de Wiart, CENAERO
- Marco Ceze, University of Michigan
- Vincent Couaillier, ONERA
- David Darmofal, MIT
- Herman Deconinck, VKI
- Charbel Farhad, Stanford University
- Chris Fidkowski, University of Michigan
- Carl Ollivier-Gooch, University of British Columbia
- Ralf Hartmann, DLR
- Koen Hillewaert, CENAERO
- Tobias Leicht, DLR
- Georg May, RWTH Aachen University
- Claus-Dieter Munz, University of Stuttgart
- Jan Nordstrom, Linköping University
- Per-Olof Persson, UC Berkeley
- Miguel Visbal, AFRL
Guidelines
- All presenters in the workshop should complete at least one sub-case from one of the 18 test cases.
- For C1 cases, hp-adaptations are required to obtain an accurate “exact” solution for error computation unless entropy errors are used as the indicator. For other cases, hp-refinement studies should be performed with at least three data points to demonstrate convergence characteristics.
- The cost of the computation should be expressed in work units. TauBench (here) should be run at least three times to obtain an average wall clock time T1. Then track the wall clock time taken by your CFD solver (excluding the initialization, post-processing data preparation time and file I/O time) T2. The work unit is then defined as T2/T1. When running TauBench, use the following parameters:
mpirun -np 1 ./TauBench -n 250000 -s 10
- The length scale h in all computations will be defined as
with nDOFs the total number of degrees of freedom per equation, unless otherwise specified.
- For steady problems, start your computation from a uniform free-stream unless otherwise specified. Use the L2 norm of the density residual to monitor convergence. Steady state is assumed if the initial residual is dropped by 10 orders of magnitude. For cases impossible to converge 10 orders, 8 orders can be used as a convergence criterion. For the flat plate boundary layer problem, use the L2 norm of the x-momentum residual to monitor convergence.
- For each p (order of accuracy), compute the work units for 100 residual evaluations with 250,000 degrees-of-freedom per equation. Use your finest mesh, and scale your results for 250,000 DOFs. Submit the results to the workshop e-mail address.
- Results submission: If you compute more than one case, submit your results using separate messages. Put “Case CX.X Results” in your subject line. Submit all results to: hung.t.huynh@nasa.gov.
- Computational meshes: The gmsh format is adopted for the workshop. The user’s manual for Gmsh version 2.5 is available here. Computational meshes in the same refinement sequence are solicited from the participants (but not required to participate). Good meshes will be posted on the web site to serve as common meshes for all participants. If you generate new meshes, please adhere to the following guideline: For all 2d external flow problems, the far field should be a circle, centered at the airfoil mid chord (or the 1st airfoil) with a radius of 1000 chords. Do not apply any vortex correction at the far field.
- Residual definition for convergence monitoring
It is not trivial to define a residual easily computable for all methods. Consider:
The integration of the equation on element Vi is
Now replacing the normal flux term with any Riemann flux as the numerical flux, we obtain
where Qi is the reconstructed approximate solution on Vi, and Qi+ is the solution outside Vi. The element residual is defined as
Then the L2 norm of the residual is defined as
where N is the total number of elements or cells. For a node based finite difference method, it is ok to use
as the residual definition. These two definitions are expected to differ by a second order term. Furthermore, note that the definition of Resi above is an example only. For different equations and different discretizations considered the definition of Resi needs to be modified to coincide with the discretization-specific residual of the scheme.
- Error computation
For any solution variable (preferably non-dimensional) s, the L2 error is defined as (Option 1)
- For an element or cell based method (FV, DG, etc.), where a solution distribution is available on the element, the element integral should be computed with a quadrature formula of sufficient precision, such that the error is nearly independent (with 3 significant digits) of the quadrature rule. Note that for a FV method, the reconstructed solution should be the same as that used in the actual residual evaluation.
- For a finite difference scheme, if the Jacobian matrix is available, i.e.,
the L2 error is defined as (Option 2a)
Otherwise, the L2 error is defined as (Option 2b)
For some numerical methods, an error defined based on the cell-averaged solution may reveal super-convergence properties. In such cases, we suggest another definition (Option 3a)
In this definition, one can also drop the volume in a similar fashion to the definition for finite-difference type methods, i.e., (Option 3b)