Interpolation with restrictions -- role of the boundary conditions and individual restrictions

0582254 - MÚ 2024 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Valášek, Jan - Sváček, P.
Interpolation with restrictions -- role of the boundary conditions and individual restrictions.
Programs and Algorithms of Numerical Mathematics 21. Vol. 21. Prague: Institute of Mathematics CAS, 2023 - (Chleboun, J.; Kůs, P.; Papež, J.; Rozložnı́k, M.; Segeth, K.; Šı́stek, J.), s. 281-292. ISBN 978-80-85823-73-8.
[Programs and Algorithms of Numerical Mathematics /21./. Jablonec nad Nisou (CZ), 19.06.2022-24.06.2022]
Grant ostatní: AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institucionální podpora: RVO:67985840
Klíčová slova: interpolation * Lagrange multiplier * Lagrange projection
Obor OECD: Pure mathematics
http://dx.doi.org/10.21136/panm.2022.26

The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative method not respecting conservation laws, a conservative interpolation method introducing constraints is described. The constraints have form of Lagrange multipliers enforcing conservation of desired flow quantities, like e.g. total fluid mass, flow kinetic energy or flow potential energy. Then the interpolation problem turns into an error minimization problem, such that the resulting quantities of proposed interpolation satisfy these physical properties while staying as close as possible to the results of Lagrangian interpolation in the L2 norm. The proposed interpolation scheme does not impose any restrictions on mesh generation process and it has a relatively low computational cost. The implementation details are discussed and test cases are shown.
Trvalý link: https://hdl.handle.net/11104/0350350