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

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    0582254 - MÚ 2024 RIV CZ eng C - Conference Paper (international conference)
    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 - others:AV ČR(CZ) AP2101
    Program: Akademická prémie - Praemium Academiae
    Institutional support: RVO:67985840
    Keywords : interpolation * Lagrange multiplier * Lagrange projection
    OECD category: 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.
    Permanent Link: https://hdl.handle.net/11104/0350350

     
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