Radar sounders (RS) are active instruments that have proved to be able to profile the subsurface of planetary bodies. The design of RS instruments, as well as the interpretation of the acquired data, is a non-trivial task due to the complexity of the scenario of acquisition and the limited amount of information on the targets (especially in planetary exploration). In this context, data simulations are necessary to support the design of the radar, the development of the related processing chain, and the definition of algorithms for the automatic analysis of data. However, state-of-the-art RS simulation methods are characterized by different trade-offs between simulation accuracy and computational costs. On the one hand, numerical methods, such as the Finite-Difference Time-Domain (FDTD) technique, allow to accurately model the wave-target interaction by exactly solving Maxwell's equations at the cost of very high computational requirements. On the other hand, optical methods, such as the ray-tracing based Multi-layer Coherent Simulator (MCS), rely on approximated solution of Maxwell's equations that allow for a better usage of computational resources at the cost of a less accurate modeling. Moreover, simulators produce raw or range-compressed only data, making it difficult to interpret and analyze them via direct comparison with the real data, which are typically processed also for azimuth compression. In this thesis, we present four main contributions related to the simulation of RS data to address the above-mentioned limitations. The first and second contributions thus present 3D simulations of selected targets of two new RS instruments, i.e., the Radar for Icy Moon Exploration (RIME) and the EnVision Subsurface Radar Sounder (SRS). The simulations are performed with the FDTD and MCS simulators. Despite producing good results in terms of detection probability of the selected targets, these two contributions highlight the above-mentioned gaps in the literature of simulation of RS data. The first main limitation is the lack of methods that can accurately model both large and small-scale scattering phenomena at relatively low computational costs. This problem is addressed by the third contribution of this thesis, which presents a novel integrated simulation technique that models both large and small-scale surface scattering phenomena by combining the advantages of the FDTD and MCS techniques, in an accurate and computationally efficient way. The second problem identified is the lack of SAR processing techniques to be applied to the simulated radargrams. This is addressed in the fourth contribution which presents a range-Doppler method for focusing raw radar sounder data simulated with 3D coherent electromagnetic simulators. The method is general and can be applied to any electromagnetic simulator, and is demonstrated for both the FDTD and MCS methods. The results presented throughout the thesis indicate that the proposed methods advance the state-of-the-art of techniques for both generating and processing simulated RS data.

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Nous développons dans ce travail de thèse un outil de simulation numérique pour les matériaux à changement de phase (MCP), en tenant compte du phénomène de convection naturelle dans la phase liquide, pour des configurations en deux et trois dimensions. Les équations de Navier-Stokes incompressible avec le modèle de Boussinesq pour la prise en compte des forces de flottabilité liées aux effets thermiques, couplées avec une formulation de l’équation d’énergie suivant la méthode d’enthalpie, sont résolues par une méthode d’éléments finis adaptatifs. Une approche mono-domaine, consistant à résoudre les mêmes systèmes d’équations dans les phases solide et liquide, est utilisée. La vitesse est ramenée à zéro dans la phase solide, en introduisant un terme de pénalisation dans l’équation de quantité de mouvement, suivant le modèle de Carman-Kozeny, consistant à freiner la vitesse à travers un milieu poreux. Une discrétisation spatiale des équations utilisant des éléments finis de Taylor-Hood, éléments finis P2 pour la vitesse et éléments finis P1 pour la pression, est appliquée, avec un schéma d’intégration en temps implicite d’ordre deux (GEAR). Le système d’équations non-linéaires est résolu par un algorithme de Newton. Les méthodes numériques sont implémentées avec le logiciel libre FreeFem++ (www.freefem.org), disponible pour tout système d’exploitation. Les programmes sont distribués sous forme de logiciel libre, sous la forme d’une forme de toolbox simple d’utilisation, permettant à l’utilisateur de rajouter d’autres configurations numériques pour des problèmes avecchangement de phase. Nous présentons dans ce manuscrit des cas de validation du code de calcul, en simulant des cas tests bien connus, présentés par ordre de difficulté croissant : convection naturelle de l’air, fusion d’un MCP, le cycle complet fusion-solidification, chauffage par le bas d’un MCP, et enfin, la solidification de l’eau. / In this thesis we develop a numerical simulation tool for computing two and three-dimensional liquid-solid phase-change systems involving natural convection. It consists of solving the incompressible Navier-Stokes equations with Boussinesq approximation for thermal effects combined with an enthalpy-porosity method for the phase-change modeling, using a finite elements method with mesh adaptivity. A single-domain approach is applied by solving the same set of equations over the whole domain. A Carman-Kozeny-type penalty term is added to the momentum equation to bring to zero the velocity in the solid phase through an artificial mushy region. Model equations are discretized using Galerkin triangular finite elements. Piecewise quadratic (P2) finite-elements are used for the velocity and piecewise linear (P1) for the pressure. The coupled system of equations is integrated in time using a second-order Gear scheme. Non-linearities are treated implicitly and the resulting discrete equations are solved using a Newton algorithm. The numerical method is implemented with the finite elements software FreeFem++ (www.freefem.org), available for all existing operating systems. The programs are written and distributed as an easy-to-use open-source toolbox, allowing the user to code new numerical algorithms for similar problems with phase-change. We present several validations, by simulating classical benchmark cases of increasing difficulty: natural convection of air, melting of a phase-change material, a melting-solidification cycle, a basal melting of a phase-change material, and finally, a water freezing case.