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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 7, Pages 1203–1217 (Mi zvmmf10068)  

This article is cited in 8 scientific papers (total in 8 papers)

Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems

A. V. Vasyukov, A. S. Ermakov, I. B. Petrov, A. P. Potapov, A. V. Favorskaya, A. V. Shevtsov

Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

Abstract: A combined method blending the advantages of smoothed particles hydrodynamics (SPH) and the grid-characteristic method (GCM) is proposed for simulating elastoplastic bodies. Various grid methods, including the GCM, have long been used for the numerical simulation of elastoplastic media. This method applies to the simulation of wave processes in elastic media, including elastic impacts, in which case an advantage is the use of moving tetrahedral meshes. Additionally, fracture processes can be simulated by applying various fracture criteria. However, this is a technically complicated task with the accuracy of the results degrading due to the continual updating of the grid. A more suitable approach to the simulation of processes involving substantial fractures and deformations is based on SPH, which is a meshless method. However, this method also has shortcomings: it produces spurious modes, and the simulation of oscillations requires particle refinement. Thus, two families of methods are available that are optimal as applied to two different groups of problems. However, a realworld problem can frequently be a mixed one, which requires a substantial tradeoff in the numerical methods applied. Aimed at solving such problems, a combined GCM-SPH method is developed that blends the advantages of two constituting techniques and partially eliminates their shortcomings.

Key words: grid-characteristic method, smoothed particles hydrodynamics, numerical simulation, unstructured meshes, combined method, high-performance computer systems, three-dimensional dynamical problems.

DOI: https://doi.org/10.7868/S0044466914070114

Full text: PDF file (1373 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:7, 1176–1189

Bibliographic databases:

UDC: 519.634
MSC: 74B20,65M25
Received: 24.01.2014

Citation: A. V. Vasyukov, A. S. Ermakov, I. B. Petrov, A. P. Potapov, A. V. Favorskaya, A. V. Shevtsov, “Combined grid-characteristic method for the numerical solution of three-dimensional dynamical elastoplastic problems”, Zh. Vychisl. Mat. Mat. Fiz., 54:7 (2014), 1203–1217; Comput. Math. Math. Phys., 54:7 (2014), 1176–1189

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. K. A. Beklemysheva, A. A. Danilov, I. B. Petrov, V. Yu. Salamatova, Yu. V. Vassilevski, A. V. Vasyukov, “Virtual blunt injury of human thorax: age-dependent response of vascular system”, Russ. J. Numer. Anal. Math. Model, 30:5 (2015), 259–268  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. B. Petrov, A. V. Favorskaya, A. V. Shevtsov, A. V. Vasyukov, A. P. Potapov, A. S. Ermakov, “Combined method for the numerical solution of dynamic three-dimensional elastoplastic problems”, Dokl. Math., 91:1 (2015), 111–113  crossref  mathscinet  zmath  isi  elib  scopus
    3. Yu. V. Vassilevski, K. A. Beklemysheva, G. K. Grigoriev, A. O. Kazakov, N. S. Kulberg, I. B. Petrov, V. Yu. Salamatova, A. V. Vasyukov, “Transcranial ultrasound of cerebral vessels in silico: proof of concept”, Russ. J. Numer. Anal. Math. Model, 31:5 (2016), 317–328  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. Petrov, “Computational problems in arctic research”, International Conference on Computer Simulation in Physics and Beyond 2015, Journal of Physics Conference Series, 681, IOP Publishing Ltd, 2016, 012026  crossref  mathscinet  isi  scopus
    5. M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70  mathnet  elib
    6. V. A. Gasilov, A. S. Grushin, A. S. Ermakov, O. G. Olkhovskaya, I. B. Petrov, “Modelirovanie razrusheniya polimernykh materialov pod deistviem intensivnykh potokov energii”, Matem. modelirovanie, 30:7 (2018), 61–78  mathnet
    7. A. V. Favorskaya, I. B. Petrov, “Theory and practice of wave processes modelling”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 1–6  crossref  mathscinet  isi  scopus
    8. A. V. Favorskaya, I. B. Petrov, “Grid-characteristic method”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, eds. A. Favorskaya, I. Petrov, Springer-Verlag, Berlin, 2018, 117–160  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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