CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

ADVANCED METHODS AND MULTIPHYSICS
(a) Schematic view of the embedded-LES approach.
(b) elsA vertical velocity (top) with the experimental data
(bottom) in the symmetry plane.
FIG. 4.2: Jet in cross flow : embedded LES simulation.
France (renamed Worms last year) to perform optimizations.
The first part is dedicated to optimization algorithms, in collaboration with the CERFACS Parallel
Algorithms team. Many different metamodels have been tested in a trust-region algorithm [CFD157] and the
impact of noisy data on stopping criteria have been studied [CFD139]. After a first study of gradient-based
algorithms in the previous years to handle the resolution of optimization problems without constraints or
with bound constraints, the introduction of general (non-linear) constraints has been considered [CFD158].
The second part is dedicated to the CFD solver and tools. A high-fidelity solver is required to compute the
objective function. The choice of the optimization algorithm is heavily constrained by the computational
cost implied by one function evaluation [CFD77]. Thus, gradient-based optimization algorithms are
particularly valued for their speed of convergence although they only give a local optimum. Therefore, the
gradient of the objective function with respect to the shape variables is computed through the discrete adjoint
method that only requires a linear system resolution for each function and constraint. As a consequence,
many numerical features have been linearized and integrated in the elsA software to enable optimizations
on complex aircraft configurations [CFD157].
The third part (the formulation of the optimization problem) is heading gradually towards MDO
(Multidisciplinary Design Optimization). A PhD student (F. Gallard) currently investigates the multipoint
optimization and the integration of aeroelastic effects for the design of flexible aircrafts. CERFACS also
takes part since 2010 in the OSYCAF project funded by the STAE foundation. The objective is to setup
a MDO methodology for an aero-structural optimization process in collaboration with : Onera, ISAE and
UPS.
4.1.3 GMRES (M. Montagnac, X. Pinel)
A Jacobian-Free Newton-Krylov framework has been developed in the elsA software and validated on
many configurations for both structured and unstructured grids [CFD161]. In this method the Jacobian
matrix does not have to be explicitly expressed as in the standard LU-SSOR method for example. Indeed,
the former relies only on the matrix-vector product of the Jacobian matrix times a vector that is implemented
simply through the computation of the flux balance. As high-order schemes are developed in parallel,
this framework will be automatically compatible contrary to the LU-SSOR method that is expected to
be changed due to its first-order linearisation scheme. Moreover, this framework may help the convergence
in case of highly skewed meshes.
158 Jan. 2010 – Dec. 2011