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## Archive of Issues

Russia Izhevsk
Year
2014
Issue
4
Pages
64-75
 Section Mathematics Title Conservative interpolation method between non-matching surface meshes Author(-s) Karavaev A.S.a, Kopysov S.P.a, Kuz'min I.M.a Affiliations Institute of Mechanics, Ural Branch of the Russian Academy of Sciencesa Abstract In this paper, we consider a problem of conservative interpolation data between non-matching surface meshes. We develop a new interpolation method based on voxel representation of the mesh followed by the evaluation of intersection area of each voxel with mesh cells. The mass of cells of the resulting mesh is represented through a linear combination of the known mass of parent cells. The method allows us to consider the problem of interpolation on curved surfaces when it is impossible to define the grid cells geometric intersection. The method was validated by numerical simulation of data interpolation based on various functions for the non-matching meshes describing plane and curved surfaces. The method of voxel interpolation was compared to the interpolation algorithm based on radial basis functions of different smoothness degree. Keywords conservative interpolation, voxel mesh, non-matching surface mesh UDC 519.65 MSC 65D05 DOI 10.20537/vm140405 Received 1 November 2014 Language Russian Citation Karavaev A.S., Kopysov S.P., Kuz'min I.M. Conservative interpolation method between non-matching surface meshes, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 4, pp. 64-75. References Garimella R., Kucharik M., Shashkov M. An efficient linearity and bound preserving conservative interpolation (remapping) on polyhedral meshes, Computers and Fluids, 2007, vol. 36, issue 2, pp. 224-237. Berndt М., Breil J., Galera S., Kucharik М., Maire P., Shashkov M. Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods, Journal of Computational Physics, 2011, vol. 230, issue 17, pp. 6664-6687. Aganin A.A., Kuznetsov V.B. Method of conservative interpolation for integral parameters of cells for arbitrary meshes, Dinamika obolochek v potoke, Kazan Physical Technical Institute of the Academy of Sciences of USSR, 1985, no. 18, pp. 144-160 (in Russian). Farrell P.E., Piggott M.D., Pain C.C., Gorman G.J., Wilson C.R. Conservative interpolation between unstructured meshes via supermesh construction, Computer Methods in Applied Mechanics and Engineering, 2009, vol. 198, no. 8, pp. 2632-2642. Azarenok B.N. A method for conservative remapping on hexahedral meshes, Mathematical Models and Computer Simulations, 2009, vol. 1, issue 1, pp. 51-63. Karavaev A.S., Kopysov S.P. The method of unstructured hexahedral mesh generation from volumetric data, Komp. Issled. Model., 2013, vol. 5, no. 1, pp. 11-24 (in Russian). Paar C., Pelzl J., Preneel B. Understanding cryptography: a textbook for students and practitioners, Heidelberg-Dordrecht-London-New York: Springer, 2011, 372 p. Buhmann M.D. Radial basis functions: theory and implementations, Cambridge: Cambridge University Press, 2004, 257 p. Kopysov S.P., Kuzmin I.M., Tonkov L.E. Methods of mesh deformation for FSI problems, Vychislitel’nye Metody i Programmirovanie, 2013, vol. 14, no. 3, pp. 269-278 (in Russian). Full text