## Section:
Overall Objectives2>
### Highlights of the Year3>
Many achievements in rocket science have been made since Apollo, but prediction of the heat flux to the
surface of spacecraft remains an imperfect science, and inaccuracies in these predictions can be fatal for the
crew or the success of robotic missions. Predicting an accurate heat flux is a particularly complex task,
regarding uncertainty on the complex multi-physics phenomena involved in hypersonic flows models as well
as on atmospheric properties such as density and temperature. Hence, it is difficult to establish “error bars”
on the heat flux prediction. We succeded the first call for project from ESA concerning uncertainty quantification for aerospace applications. In this project, we are the main investigator concerning the set-up of efficient numerical techniques for UQ.

In June and July, we joined the NASA Center for Turbulence Research (CTR) Summer Program at Stanford University. We developed a novel method to solve stochastic partial differential equations, in particular hyperbolic equations.

We have developed an algorithm for the robust construction of curved simplicial meshes in two and three dimensions.
Starting from a classical (straight) mesh, we are able to curve the boundary elements then the volumic ones in keeping
as much as possible the structure of the initial mesh. In particular, this algorithm does not destroy the boundary layer structures, even for meshes designed for turbulent simulations.

We have succeded in having Residual Distribution schemes that are *uniformly* accurate whatever the Peclet number for scalar advection diffusion problems. The schemes have been extended to turbulent flow simulations.

The native scheduler of the PaStiX solver can be replaced with
generic runtimes to address sparse direct factorizations on heterogeneous
architectures (clusters of multicore/multigpu). Our results on
heterogeneous architectures show we can easily improve the factorization
time on a personal computer (1 GPU and several cores), and we have
identified leads, both on algorithms and on schedulers, to optimize
the performances on larger platforms.

Many achievements in rocket science have been made since Apollo, but prediction of the heat flux to the surface of spacecraft remains an imperfect science, and inaccuracies in these predictions can be fatal for the crew or the success of robotic missions. Predicting an accurate heat flux is a particularly complex task, regarding uncertainty on the complex multi-physics phenomena involved in hypersonic flows models as well as on atmospheric properties such as density and temperature. Hence, it is difficult to establish “error bars” on the heat flux prediction. We succeded the first call for project from ESA concerning uncertainty quantification for aerospace applications. In this project, we are the main investigator concerning the set-up of efficient numerical techniques for UQ.

In June and July, we joined the NASA Center for Turbulence Research (CTR) Summer Program at Stanford University. We developed a novel method to solve stochastic partial differential equations, in particular hyperbolic equations.

We have developed an algorithm for the robust construction of curved simplicial meshes in two and three dimensions. Starting from a classical (straight) mesh, we are able to curve the boundary elements then the volumic ones in keeping as much as possible the structure of the initial mesh. In particular, this algorithm does not destroy the boundary layer structures, even for meshes designed for turbulent simulations.

We have succeded in having Residual Distribution schemes that are

*uniformly*accurate whatever the Peclet number for scalar advection diffusion problems. The schemes have been extended to turbulent flow simulations.The native scheduler of the PaStiX solver can be replaced with generic runtimes to address sparse direct factorizations on heterogeneous architectures (clusters of multicore/multigpu). Our results on heterogeneous architectures show we can easily improve the factorization time on a personal computer (1 GPU and several cores), and we have identified leads, both on algorithms and on schedulers, to optimize the performances on larger platforms.