The purpose of this article is to discuss several modern aspects of remeshing, which is the task of modifying an ill-shaped tetrahedral mesh with bad size elements so that it features an appropriate density of high-quality elements. After a brief sketch of classical stakes about meshes and local mesh operations, we notably expose (i) how the local size of the elements of a mesh can be adapted to a user-defined prescription (guided, e.g., by an error estimate attached to a numerical simulation), (ii) how a mesh can be deformed to efficiently track the motion of the underlying domain, (iii) how to construct a mesh of an implicitly-defined domain, and (iv) how remeshing procedures can be conducted in a parallel fashion when large-scale applications are targeted. These ideas are illustrated with several applications involving high-performance computing. In particular, we show how mesh adaptation and parallel remeshing strategies make it possible to achieve a high accuracy in large-scale simulations of complex flows, and how the aforementioned methods for meshing implicitly defined surfaces allow to represent faithfully intricate geophysical interfaces, and to account for the dramatic evolutions of shapes featured by shape optimization processes.

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Forecasting the physical behavior of the subsurface is a challenging task. Available data include seismic wave propagation recordings that are interpreted to build subsurface multi-material models. Due to this interpretation, the geometry and the connectivity of the interfaces separating geological materials are uncertain. In this work, we consider a relatively simple case of fluid monitoring in a subsurface gas reservoir. As seismic wave velocities of porous rocks vary depending on fluid saturation, our objective is to quantitatively evaluate the impact of the water/gas contact depth on elastic wave propagation.