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KIAM Preprint  30, Moscow, 2021
Authors: Poveschenko Y.A., Krukovskiy A. Y., Boykov D.S., Podryga V.O., Rahimly P.I.
Three-dimensional modeling of hydrodynamic problems taking into account elastic processes
Abstract:
A finite-difference approximation of elastic forces on spaced Lagrangian grids is constructed, based on the method of support operators. For displacement vectors on irregular grids, on the topological and geometric structure of which minimal reasonable restrictions are imposed, the approximations of vector analysis operations are constructed in relation to difference schemes for problems of elasticity theory. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete modeling of these processes. The schemes are considered, both using the stress tensor in an explicit form, and dividing it into spherical and shear components (pressure and deviator). The latter is used to construct homogeneous algorithms applicable to both the solid and the vaporized phase. The linear theory of elasticity is used for constructing approximations. The resulting forces in spatial geometry are obtained explicitly. Calculations of the sound waves propagation in a three-dimensional orthogonal aluminum plate due to end impact are presented. These calculations confirm the good quality of the difference schemes constructed in work.
Keywords:
support operator method, two- and three-dimensional conservative difference schemes, spaced Lagrangian grid
Publication language: russian,  pages: 15
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Poveschenko Yuri Andreevich,  orcid.org/0000-0001-9211-9057KIAM RAS
  • Krukovskiy Alexander Yurevich,  orcid.org/0000-0003-4188-6904KIAM RAS
  • Boykov Dmitri Sergeevich,  orcid.org/0000-0001-8587-4994KIAM RAS
  • Podryga Victoria Olegovna,  orcid.org/0000-0001-7874-6978KIAM RAS
  • Rahimly Parvin Ilgar gizi,  orcid.org/0000-0002-9271-5956KIAM RAS