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Preprints of the Keldysh Institute of Applied Mathematics, 2023, 007, 16 pp.
DOI: https://doi.org/10.20948/prepr-2023-7
(Mi ipmp3130)
 

Numerical modeling of spatial problems of hydrodynamics taking into account elastic processes

Yu. A. Poveshchenko, A. Yu. Krukovskiy, V. O. Podryga, P. I. Rahimly, D. S. Boykov
References:
Abstract: In the present work, the support operator method for spatial problems of elasticity theory is used to construct a finite-difference approximation of elastic forces on staggered Lagrangian meshes. For displacement vectors on irregular meshes, as applied to difference schemes, for problems of elasticity theory, the corresponding discrete operations have been developed. Taking into account the energy balance of the medium, the presented families of integrally consistent approximations of vector analysis operations are sufficient for numerical modeling of these processes. The resulting forces acting on the nodal domains of the medium are obtained explicitly in two-dimensional and three-dimensional geometry. Calculations are given for the propagation of sound waves in an aluminum three-dimensional orthogonal plate due to an end impact. On the example of numerical calculations, the invariance of the elastic force and energy characteristics of the medium during solid-state rotations is confirmed.
Keywords: support operator method, two-dimensional and three-dimensional conservative finite-difference schemes, Lagrangian staggered mesh.
Funding agency Grant number
Russian Foundation for Basic Research 20-51-18004-Болг_а
The reported study was funded by RFBR and National Science Foundation of Bulgaria (NSFB), project number 20-51-18004.
Document Type: Preprint
Language: Russian
Citation: Yu. A. Poveshchenko, A. Yu. Krukovskiy, V. O. Podryga, P. I. Rahimly, D. S. Boykov, “Numerical modeling of spatial problems of hydrodynamics taking into account elastic processes”, Keldysh Institute preprints, 2023, 007, 16 pp.
Citation in format AMSBIB
\Bibitem{PovKruPod23}
\by Yu.~A.~Poveshchenko, A.~Yu.~Krukovskiy, V.~O.~Podryga, P.~I.~Rahimly, D.~S.~Boykov
\paper Numerical modeling of spatial problems of hydrodynamics taking into account elastic processes
\jour Keldysh Institute preprints
\yr 2023
\papernumber 007
\totalpages 16
\mathnet{http://mi.mathnet.ru/ipmp3130}
\crossref{https://doi.org/10.20948/prepr-2023-7}
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    Препринты Института прикладной математики им. М. В. Келдыша РАН
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