Adjoint-based optimization of two-dimensional Stefan problems
| Autor: | Tomas Fullana, Vincent Le Chenadec, Taraneh Sayadi |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Fluid Dynamics (physics.flu-dyn) FOS: Physical sciences Physics - Fluid Dynamics Mathematical Physics (math-ph) Numerical Analysis (math.NA) Computational Physics (physics.comp-ph) Computer Science Applications Computational Mathematics Modeling and Simulation FOS: Mathematics Mathematics - Numerical Analysis Physics - Computational Physics Mathematical Physics |
| Zdroj: | Journal of Computational Physics. 475:111875 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2022.111875 |
| Popis: | A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary (cut cell) method coupled with an implicit time-advancement scheme is employed to solve the heat equation. A conservative implicit-explicit scheme is then used for solving the level set transport equation. The resulting numerical framework is validated with respect to existing analytical solutions of the forward Stefan problem. An adjoint-based algorithm is then employed to efficiently compute the gradient used in the optimisation algorithm (L-BFGS). The algorithm follows a continuous adjoint framework, where adjoint equations are formally derived using shape calculus and transport theorems. A wide range of control objectives are presented, and the results show that using parameterised boundary actuation leads to effective control strategies in order to suppress interfacial instabilities or to maintain a desired crystal shape. Comment: 33 pages, 16 figures, preprint submitted to Journal of Computational Physics |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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