Program: FP7-AAT-2013-RTD-1

Grant Agreement Number 605036

Started : 1st October 2013. Duration 36 months.

This work was partly done in the UMRIDA project which is supported by the European Commission under contract No. ACP3-GA-2013-605036.

The authors gratefully acknowledge GENCI for granted access to HPC resources through IDRIS (France) and CINES (France).

This work was partly done in the MAIDESC ANR project which is supported by the french ministery of Research under contract ANR-13-MONU-0010.

Partners:

NUMECA INTERNATIONAL (Coordinator )

DASSAULT AVIATION SA, Paris

EASN Technology Innovation Services BVBA, BÜDINGEN (B)

ALENIA AERMACCHI SPA, Torino

MAN DIESEL & TURBO SCHWEIZ AG, Zurich

TURBOMECA SA, Bordes (F)

NPO SATURN OAO, Rybinsk

ESTECO SPA, Trieste

OFFICE NATIONAL D'ETUDES ET DE RECHERCHES AEROSPATIALES, Chatillon (F)

DEUTSCHES ZENTRUM FUER LUFT - UND RAUMFAHRT EV, Koeln

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE, Rocquencourt (F)

CENTRE INTERNACIONAL DE METODES NUMERICS EN ENGINYERIA, Barcelona

CENTRE EUROPEEN DE RECHERCHE ET DE FORMATION AVANCEE EN CALCUL SCIENTIFIQUE, Toulouse

TECHNISCHE UNIVERSITEIT DELFT, Delft

VRIJE UNIVERSITEIT BRUSSEL, Brussel

POLITECHNIKA WARSZAWSKA, Warsaw

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE, Lausanne

LINKÖPINGS UNIVERSITET, Linköping

EUROPEAN AERONAUTIC DEFENCE AND SPACE COMPANY EADS FRANCE SAS, Paris

TECHNISCHE UNIVERSITAET DRESDEN, Dresden

Scientific role of INRIA:

Probabilistic models for numerical outputs : models for numerical errors, models for physical model errors

Convergence, error estimates, correctors for mesh adaptive CFD calculation. Probabilistic models for approximation .

Contribution to transfer of knowledge

Review of strategies for addressing uncertainties by differentiation. Application of the symbolic Differentiation tool TAPENADE .

Role of Partner INRIA:

Responsible of:

Workpackage 2 (M1-24): Improvement of methods for Uncertainty Quantification towards industrial readiness

Responsible of Task 2.3

Task 2.1 (coord. Chris Lacor (Chris.Lacor@vub.ac.be), VUB): UQ methods for efficient handling of large number of uncertainties

In NODESIM, Dassault and INRIA has demonstrated the efficiency of the TAPENADE tool for developing second derivatives of CFD kernels. Based on this, INRIA will define, in cooperation with AAEM, a strategy for improving the second-order differentiation of industrial CFD codes for a large number of parameters. This will involve (i) a discussion of the differentiation formula to choose, which depends on linear solution cost and number of parameters, (ii) the identification of an extra level in parallelism (cf. State of art) and (iii) a proposition for efficient solutions of a linear system with multiple right-hand sides, including experimenting a coarse grid system factorization. INRIA will extend his Automatic Differentiation tool in order to produce second derivatives for parallel MPI software and make it available to UMRIDA partners. Lastly, INRIA will assist AAEM in the efficient differentiation of its Euler/Navier Stokes UNS3D code in reverse mode.

D2.1- 06 (11) INRIA 6 R CO Report proposing a strategy for the differentiation of CFD codes for a large number of uncertainties

Task 2.2 (coord. Jacek Rokicki(jack@meil.pw.edu.pl), Lukasz Laniewski-Wollk (llaniewski@meil.pw.edu.pl) , WUT): Development of efficient UQ methods for general geometrical uncertainties

INRIA will assist AAEM in the application of Automatic Differentiation to the AAEM software, dealing with geometrical uncertainties.

Task 2.3 (coord. A. Dervieux): Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods

Partners involved:

      ONERA: Jacques Peter (Jacques.Peter@onera.fr)

      Linkoping (LIU): Jan Nordström (jan.nordstrom@liu.se)

INRIA contribution to Task 2.3:

UQ for Numerical error: INRIA will develop a method proposing a probabilistic law for the numerical error. A 3D RANS kernel will be the starting of the study. For this kernel, the norm-oriented mesh optimization method will be applied. This novel method extends the minimization of a scalar input error of the goal-oriented technology to the minimization of the deviation between approximated and exact solution in some norm to be chosen by user. It can be shown that the resulting optimum anisotropic mesh enjoys high-order convergence to continuous solution, which consolidates the accuracy of the error estimate. From this, an error model will be defined as a Gaussian random variable with a standard deviation related to the a posteriori error estimate. This error will be evaluated over the several adapted meshes used for mesh convergence in order to validate and calibrate the proposed approach. The IC-02 and IC-03 aircraft geometries will be the basis of the demonstration of the new approach and of the partner contribution to database and workshop. The calibration of the new method will then be performed on this test case from a mesh convergent sequence of calculations.

UQ for Model errors: As indicated in section B.1.2.3.3, the perturbation analysis of the flow with respect to the turbulent viscosity coefficient correlates well with the model error and therefore can be useful for modelling it. INRIA will work in coordination with Dassault on the study of this kind of model and its interaction with numerical errors and geometry variation. The study will focus on the evaluation of the derivative of flow and scalar input with respect to viscosity constant for a one equation RANS. The approximation error on this sensitivity will also be evaluated. The IC-02 aircraft and IC-03 Falcon geometries will be the basis of the demonstration of the new approach and of the partner contribution to database and workshop. The calibration of the new method will then be performed on this test case (in cooperation with Dassault) and give a probabilistic model for the standard deviation of modelling error. Merging of Uncertainties: Both numerical and model errors proposed by INRIA and Dassault will be of similar definition to usual uncertainty probabilistic description. This will render applicable a merging of the three types of uncertainties in a robust analysis and design process. Dassault and INRIA will define and test a method for this multi-uncertainty fusion, experimenting first the superposition of the errors in a quadratic functional (only the propagation of the design/flight condition need be solved propagated). Dassault and INRIA will test this approach on the IC-03 case and for a M6 wing test case for which many wind tunnel measurements are available.

D2.3- 24 (11) INRIA 24 R CO UQ methods for numerical and model CFD errors

WP 3: Validation and Evaluation of UQ methods for Industrial Challenges (M6-M36)

Task 3.2 (coord. Franck Nicoud (franck.nicoud@univ-montp2.fr)) UM2): Application of methods of WP2 to the selected test cases

INRIA will compute the test case IC-03 (Generic Falcon Jet configuration) proposed by Dassault with a RANS 3D kernel. For these two test cases, INRIA will produce a random model of numerical error based on the adjoint-based adaptive mesh convergence and adjoint-based correction method.

WP 5: Exploitation, Dissemination, Workshop, BP Guide for end-users (M6-M36)

Task 5.1 (coord. Dirk Wunsch (dirk.wunsch@numeca.be) NUMECA): Workshops on UQ and Robust Design

INRIA will present to the workshops the results of its WP3 contribution, flows around regional and Business aircrafts.

Task 5.2 (coord. Gabriel Bugeda (bugeda@cimne.upc.edu) CIMNE) : Best Practice Guide for UQ and Robust design

INRIA will contribute to the Best Practice Guide in particular for adjoint-based perturbation methods including the use of Automatic Differentiation, and for the integration of error models in uncertainty management.

Task 5.3 (coord. Myrto Zacharaki (myrto.zacharaki@easn.net) EASN): Dissemination and exploitation actions

INRIA will give publicity to the UMRIDA outputs in some scientific meetings, which INRIA co-organizes. A particular emphasis will be put on publishing (by papers or tutorials) the new applications of adjoint- based methods in the Euro AD workshop, organized by Autodiff (www.autodiff.org).

Presentations by INRIA: