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

COMPUTATIONAL FLUID DYNAMICS
FIG. 2.12: Conjugate heat transfer prediction obtained by use of a massively parallel solution applied to a
gas turbine combustor : field of wall temperature complemented by an iso-surface of temperature, allowing
to visualize the flame position in the LES instantaneous prediction used in the coupled solution.
2.4 Methods
2.4.1 Numerics (M. Kraushaar, L. Gicquel, V. Moureau, G. Wang, F. Duchaine,
L. Giraud)
Numerical schemes for LES require certain properties, i.e. low-diffusion schemes of high-order of accuracy
so as not to interfere with the turbulence models. To meet this purpose in the context of fully unstructured
solvers, a new family of high-order time-integration schemes with adjustable diffusion has been proposed
by M. Kraushaar in his thesis, in collaboration with CORIA (V. Moureau) [CFD182].
Another aspect is the comparison of compressible and incompressible formulations. Being fully unsteady by
nature, LES is very consuming in terms of CPU time and a possible way to decrease this cost for low-speed
flows is to use low-Mach or incompressible formulations, allowing much larger convective time-steps. This
is of particular interest for the simulation of combustors, where the flow velocities stay often low. The impact
of the incompressibility assumption and the different nature of the numerical algorithms have also been
addressed in the PhD of M. Kraushaar, where detailed comparisons of a fully explicit compressible solver
and an incompressible solution developed at CORIA (YALES2 code) are proposed for an experimental
swirled configuration representative of a real burner.
Work has also been done on the AVTP solver, for heat conduction in solid media. In order to relax the
time step constraint imposed by the Fourier condition on the explicit scheme implemented in AVTP, an
unconditionally stable implicit scheme has been implemented . Using the mesh partitioning parallelism
of AVTP and adapting the existing numerical kernels, matrix-free parallel linear solvers were designed
for the linear systems involved in implicit schemes. These linear solvers are based on Krylov subspace
techniques, namely un-preconditioned Conjugate Gradient and un-preconditioned GMRES. Even though
implicit schemes enable significant decrease of the parallel elapsed time for AVTP, up-to a speed-up of 200,
further improvement will be gained by preconditioning techniques. To this purpose, scalable preconditioners
will be designed, having a convergence behaviour independent of the number of subdomains and weakly
dependent on the subdomain size.
CERFACS ACTIVITY REPORT 143