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Article Dans Une Revue Journal of Computational Physics Année : 2024

Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity

Résumé

We propose an automated nonlinear model reduction and mesh adaptation framework for rapid and reliable solution of parameterized advection-dominated problems, with emphasis on compressible flows. The key features of our approach are threefold: (i) a metric-based mesh adaptation technique to generate an accurate mesh for a range of parameters, (ii) a general (i.e., independent of the underlying equations) registration procedure for the computation of a mapping Φ that tracks moving features of the solution field, and (iii) an hyper-reduced least-square Petrov-Galerkin reduced-order model for the rapid and reliable estimation of the mapped solution. We discuss a general paradigm — which mimics the refinement loop considered in mesh adaptation — to simultaneously construct the high-fidelity and the reduced-order approximations, and we discuss actionable strategies to accelerate the offline phase. We present extensive numerical investigations for a quasi-1D nozzle problem and for a two-dimensional inviscid flow past a Gaussian bump to display the many features of the methodology and to assess the performance for problems with discontinuous solutions.

Dates et versions

hal-04371531 , version 1 (03-01-2024)

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Paternité

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Nicolas Barral, Tommaso Taddei, Ishak Tifouti. Registration-based model reduction of parameterized PDEs with spatio-parameter adaptivity. Journal of Computational Physics, 2024, 499, pp.112727. ⟨10.1016/j.jcp.2023.112727⟩. ⟨hal-04371531⟩
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