Section: New Results

Numerical methods for high altitude aerodynamics and rarefied gas flows

Participants : Luc Mieussens [Corresponding member] , Florent Pruvost [IMB, engineer] , G. Dechristé [IMB, PhD] , N. Hérouard [CEA-CESTA, PhD] , Stéphane Brull [IMB] , L. Forestier-Coste [IMB, Post Doc] .

This activity involves many developments for rarefied gas flow simulations for very different applications, and the design of numerical schemes for high altitude aerodynamics based on some kinetic model :

• the simulation code CORBIS (rarefied gases in 2 space dimensions on structured meshes) has been re-engineered : modular form, use of the git version control system, modification to use unstructured meshes, MPI/OpenMP hybrid parallelization. Very good performance in terms of scalability and efficiency have been obtained, up to 700 cores.

• a new method to generate locally refined grids in the space of velocities has been proposed and shown to provide CPU time gains of the order of 30 (w.r.t the existing approach). This work has been published in (Baranger et al., J. Comput. Phys 257(15), 2014)  ;

• the second order Discontinuous Galerkin method has been shown to be more accurate and faster than higher order finite volume methods (up to fourth order) for one-dimensional rarefied gases problems. We have analytically proved that this method is Asymptotic Preserving for the Stokes regime ;

• a new kinetic model for multispecies reacting flows for re-entry applications has been proposed. In this model, the mixture oxygen-nytrogen is described by a kinetic equation, while the minor species (O, NO, N) are described by reaction diffusion equations. The implementation of this model in a full 3D code is under way ;

• we have presented one of the first numerical simulation of the Crookes radiometer ever. This has been obtained with a Cartesian grid approach, with a cut-cell techniques allowing a simplified treatment of moving solid boundaries. This work has been published in the proceedings of the 28th Symposium on rarefied Gas Dynamics ;

• We have proposed a new method to discretize kinetic equations based on a discretization of the velocity variable which is local in time and space. This induces an important gain in term of memory storage and CPU time, at least for 1D problems (this work has been presented in a paper submitted for publication). Two-dimensional extensions are under development ;

• We have shown that the recent method “Unified Gas Kinetic Scheme”, proposed by K. Xu to simulate multi-scale rarefied gas flows, can be extended to other fields, like radiative transfer. This approach, based on a simple finite volume technique, is very general and can be easily applied to complex geometries with unstructured meshes. This work has been published in (Mieussens, et al., J. Comput. Phys 253(15), 2013).