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Argon --- Plasma --- Magnetohydrodynamique --- Argon --- Plasma --- Magnetohydrodynamique

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Spacecraft undergo severe convective and radiative heating from the surrounding aerothermodynamic environment during their atmospheric entry at high velocities. An accurate heat-flux prediction during the design of such vehicles is therefore paramount for the success and safety of future planetary missions. The numerical simulation of hypersonic reactive plasma flows coupled with radiative heat transfer is an active research topic for the design of thermal protection systems of future space missions, in particular for the Mars exploration program. The numerical simulation of radiative transfer is a challenging problem because of the spatial, angular, and spectral dependence of the radiation field. The reference approach for treating the spectral dependence is the Line-By-Line (LBL) method which consists in finely discretizing the radiative properties over the relevant spectral range. These radiative properties depend on level populations and on fundamental spectroscopic data. We propose to implement a statistical narrow band formulation into the finite-volume algorithm for radiative heat-transfer of the COOLFuiD platform to decrease the computational time. 3D radiation fields will be computed for atmospheric entries of space missions. This work is related to the ABLARADABLA project of the European Space Agency.

Radiation, spacecraft heat loads, reentries --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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The goal of the master thesis is to apply the DG-FEM (Discontinuous Galerkin Finite Element Method) to plasma flows, in particular to the plasma sheaths.

Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Since the beginning of the 20th century, research in low-temperature plasmas has grown into a major field of plasma science. In particular, confined plasmas are of great interest for a large range of technological applications: from domestic with lightning and plasma displays panels (PDPs), to electric space propulsion and, more recently, medicine. This vast domain of application gives rise to many numerical models whose specificities are adapted to current needs.

The main difficulty in plasma modelling is the very large mass disparity between electrons and the other species that compose the ionised gas. This intrinsic multiscale property makes the numerical problem very stiff. Paving the way to the need of high-resolution methods.

This work proposes the numerical simulation of a two-fluid low-temperature plasma with the use of high order Discontinuous Galerkin finite element Methods (DG-FEM). For this purpose, the coupled resolution of the electrons and ions transports equations with a Poisson's equation for the electrical potential is carried out through a fully implicit strategy. This choice permits to overcome the strict stability constraints coming from the electrons/ions mass disparity that affect explicit schemes.

Starting from the general Galerkin variational formulation, this coupled resolution of hyperbolic-elliptic equations is addressed with the implementation of specific strategies: An entropy-consistent Roe numerical flux is developed alongside incomplete internal penalty methods being applied only to the electrostatic system. An extension to the classical formulation of the implicit ESDIRK scheme is provided. Indeed, the inertia terms associate to the potential is deactivated by the introduction of a Boolean parameter which is equal to 1 for all the parameters excepts for the potential. As a result, this modification of the implicit method permits to treat the Poisson's equation alongside the fluid equations during the Newton iterator, enhancing then its convergence. An automatic evaluation of the Jacobian matrix using first-order central difference is also described with a specific treatment made onto the linearisation of the ionisation contributions. All of these strategies were implemented in the ForDGe solver, an immersed boundary Cartesian DG-FEM solver developed at the University of Liege.

Tested on two practical cases, namely: the two-stream periodic perturbation and the sheath problem, the current fully-coupled implicit DG-FEM solver is able to tackle accurately the physics of low-temperature collisionless plasma. In the case of the two-stream instability, the current implicit solver demonstrated its increased stability with resolution using time step that is more than two orders of magnitude bigger than the electron plasma frequency, one of the most stringent stability constraints for plasma flows. Non-linear behaviour of the solution is encountered when dealing with longer simulation. This can be addressed to a lack of consistency of the Roe flux at low-Mach regime.

For the plasma sheath problem, the current solver allows us to reach a steady state solution that is in very good agreement with state of the art solution, but also gives a good representation of the physics of the sheath. The steady state is achieved with the simple use of time integration, at the cost of considerable computational effort.

plasma, --- Discontinuous Galerkin --- multifluid formulation --- potential equation --- low-temperature plasma --- implicit time integration --- two-fluid model --- Ingénierie, informatique & technologie > Ingénierie aérospatiale