UMRIDA Kick-Off Meeting Brussels, october Partner 11 : INRIA

Involvement in UMRIDA WP’s WP2: Improvement of UQ methods towards industrial readiness Task 2.1: UQ methods for efficient handling of large number of uncertainties Task 2.2: Development of efficient UQ methods for general geometrical uncertainties Task 2.3: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods: UQ for Numerical error, UQ for Model errors, Merging of Uncertainties WP 3: Validation and Evaluation of UQ methods for Industrial Challenges Task 3.2: Application of methods of WP2 to the selected test cases WP 5: Exploitation, Dissemination, Workshop, BP Guide for end-users Task 5.1: Workshops on UQ and Robust Design Task 5.2: Best Practice Guide for UQ and Robust design Task 5.3: Dissemination and exploitation actions

WP2-T2.1: UQ methods for efficient handling of large number of uncertainties Cooperation with AAEM Improving the second-order differentiation of industrial CFD codes for a large number of parameters. (i) differentiation formula to choose, which depends on linear solution cost and number of parameters, (ii) the identification of an extra level in parallelism and (iii) efficient solutions of a linear system with multiple right-hand sides. INRIA will extend his Automatic Differentiation tool in order to produce second derivatives for parallel MPI software and make it available to UMRIDA partners. INRIA will assist AAEM in the efficient differentiation of its Euler/Navier Stokes UNS3D code in reverse mode. Report proposing a strategy for the differentiation of CFD codes for a large number of uncertainties (M6)

Task 2.2: 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: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods UQ for Numerical error: INRIA will develop a method proposing a probabilistic law for the numerical error in using a 3D RANS kernel. The fiability of the standard-deviation/error estimate will rely on the combination of : - mesh convergence obtained with mesh adaption, - error estimates. 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.

Task 2.3: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods (cont’d) UQ for Numerical error, cont’d: for fiable numerics, we look for : Mesh convergence of flow field at scheme order with the help of a norm-oriented metric-based mesh adaptation. Mesh convergence of error estimate.

Task 2.3: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods (cont’d) Convergences en maillage adaptatif de champs de Mach (FP6-HISAC, 2009)

Task 2.3: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods (cont’d) Mesh convergence of error estimate. Exemple : A priori error estimate for a Poisson problem in a square: 21x21 and 41x41

Task 2.3: Impact of numerical properties of CFD codes, numerical noise, including issues of shock discontinuities on assessment and validation of UQ methods UQ for Model errors for RANS: The perturbation analysis of the RANS flow with respect to the turbulent viscosity coefficient correlates with the model error and will be used 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 calibration and demonstration of the new approach and of the partner contribution to database and workshop. This will give a probabilistic model for the standard deviation of modelling error. M24: UQ methods for numerical and model CFD errors

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

WP 3: Validation and Evaluation of UQ methods for Industrial Challenges Task 3.2: 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 Task 5.1: 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: 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: Dissemination and exploitation actions: INRIA will give publicity to the UMRIDA outputs in scientific meetings, which INRIA co-organizes. A particular emphasis will be put on publishing UMRIDA outputs in the Euro AD workshop.

Thank you.