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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

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.

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

Workshop Details

Final Agenda

Download the final agenda for the workshop here.

Objectives

  1. 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.
  2. 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.
  3. To identify pacing items in high-order methods needing additional research and development in order to proliferate in the CFD community.
  4. To facilitate international collaboration and enhance mutual understanding among CFD researchers and managers in academia, government, and industries.

General Information

  1. The workshop is open to participants all over the world. Everybody is welcome.
  2. Several benchmark cases are included for the workshop. To be considered as speakers, participants should complete as least one sub-case.
  3. Open forums will be included in the workshop to discuss pacing items and further research areas in high-order methods.
  4. 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

C1.2 Flow over the NACA0012 airfoil – Summary by G. May

C1.3 Flat plate boundary layer – Summary by M. Galbraith and D. Darmofal

C1.4 Vortex transport by uniform flow – Summary by D. Caraeni

C2. Intermediate, 2D & 3D

C2.1 Turbulent flow over a RAE airfoil – Summary by K. Fidkowski

C2.2 Delta wing at low Reynolds number – Summary by R. Hartmann

C2.3 Heaving and Pitching Airfoil – Summary by P. Persson

C3. Difficult, 2D & 3D

C3.1 Turbulent flow over a multi-element airfoil – Summary by M. Ceze

C3.2 Turbulent flow over DPW III wing – Summary by M. Ceze

C3.3 Direct Numerical Simulation of the Taylor-Green Vortex – Summary by K. Hillewaert

C3.4 DNS and LES of flow over 2D periodic hill – Summary by C.C. de Wiart

C3.5 CRM wing/body – Summary by T. Leicht

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

For 2D problems    

For 3D problems     

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.,

Jacobian

the L2 error is defined as (Option 2a)

L2_error_2a

Otherwise, the L2 error is defined as (Option 2b)

L2_error_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)

L2_error_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)

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