Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries

Éléonore Gauci 1, 2
2 Gamma3 - Automatic mesh generation and advanced methods
ICD - Institut Charles Delaunay, Inria Saclay - Ile de France
Abstract : When dealing with CFD problems, mesh adaptation is interesting for its ability to approach the asymptotic convergence and to obtain an accurate prediction for complex flows at a lower cost. Anisotropic mesh adaptation method reduces the number of degrees of freedom required to reach a given solution accuracy, thus impact favorably the CPU time. Moreover, it reduces the numerical scheme dissipation by automatically taking into account the anisotropy of the physical phenomena inside the mesh. Two main approaches exist in the literature. Feature-based mesh adaptation which is mainly deduced from an interpolation error estimate using the Hessian of the chosen sensor controls the interpolation error of the sensor over the whole computational domain. Such approach is easy to set-up and has a wide range of application, but it does not take into account the considered PDE used to solve the problem. On the other hand, goal-oriented mesh adaptation, which focuses on a scalar output function, takes into consideration both the solution and the PDE in the error estimation thanks to the adjoint state. But, the design of such error estimate is much more complicated. This thesis presents the results obtained with different CFD methods : the Arbitrary Lagrangian Eulerian (ALE) flow solvers with explicit and implicit schemes are presented and coupled to the moving mesh process, the feature-based unsteady mesh adaptation for moving geometries takes into account the changes of connectivites during the whole simulation, the adjoint state is extended to moving geometries problems and goal-oriented unsteady mesh adaptation for moving meshes is derived from an a priori error estimate. Several numerical examples are considered in the aeronautics sector and the field of civil security.
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Éléonore Gauci. Goal-oriented metric-based mesh adaptation for unsteady CFD simulations involving moving geometries. Fluids mechanics [physics.class-ph]. Université Côte d'Azur, 2018. English. ⟨NNT : 2018AZUR4227⟩. ⟨tel-02272727⟩

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