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Original title:
Interpolation with restrictions -- role of the boundary conditions and individual restrictions
Authors: Valášek, Jan ; Sváček, P.
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: 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.
Keywords: interpolation; Lagrange multiplier; Lagrange projection
Project no.: AP2101
Funding provider: AV ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21, ISBN 978-80-85823-73-8
Note: Související webová stránka: http://dx.doi.org/10.21136/panm.2022.26
Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: https://hdl.handle.net/11104/0350350
Permalink: http://www.nusl.cz/ntk/nusl-539255
The record appears in these collections:
Research > Institutes ASCR > Institute of Mathematics
Conference materials > Papers
Authors: Valášek, Jan ; Sváček, P.
Document type: Papers
Conference/Event: Programs and Algorithms of Numerical Mathematics /21./, Jablonec nad Nisou (CZ), 20220619
Year: 2023
Language: eng
Abstract: 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.
Keywords: interpolation; Lagrange multiplier; Lagrange projection
Project no.: AP2101
Funding provider: AV ČR
Host item entry: Programs and Algorithms of Numerical Mathematics 21, ISBN 978-80-85823-73-8
Note: Související webová stránka: http://dx.doi.org/10.21136/panm.2022.26
Institution: Institute of Mathematics AS ČR (web)
Document availability information: Fulltext is available in the digital repository of the Academy of Sciences.
Original record: https://hdl.handle.net/11104/0350350
Permalink: http://www.nusl.cz/ntk/nusl-539255
The record appears in these collections:
Research > Institutes ASCR > Institute of Mathematics
Conference materials > Papers
Record created 2024-02-18, last modified 2024-04-15