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Matem. Mod., 2013, Volume 25, Number 8, Pages 89–108 (Mi mm3412)  

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

Numerical modeling elasto-plastic flows by using a Godunov method with moving Eulerian grids

Igor Menshova, Alexander Mischenkob, Alexey Serejkinb

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow
b All-Russian Scientific Research Institute of Automatics, Moscow

Abstract: The paper addresses a numerical method for calculating elasto-plastic flows on arbitrary moving Eulerian grids. The Prandtl-Reus model is implemented in the system of governing equations to describe elasto-plastic properties of solids in dynamical processes. The spatial discretization of the equations is carried out with the Godunov method applied to a moving Eulerian grid. Piecewise-linear cell data reconstruction is implemented using a MUSCL-type interpolation procedure with generalization on unstructured grids to improve accuracy of the scheme. The main idea of method is composed of splitting system of governing equations into hydrodynamical and elastoplastic components. The hydrodynamical part of equations is updated in time with an absolutely stable explicit-implicit time marching scheme. The solution to the constitutive equations is obtained with the second order Runge–Kutta scheme. The theoretical analysis is carried out and analytical solutions are presented that describe the shock-wave structure and the structure of a rarefaction wave in elasto-plastic materials under uniaxial deformation assumption. The method is verified by calculating the problems with presented analytical solutions, and also comparing on some test problems calculated by other authors with different numerical methods.

Keywords: Godunov numerical method, elasto-plastic flow, moving computational grid.

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English version:
Mathematical Models and Computer Simulations, 2014, 6:2, 127–141

Bibliographic databases:

Received: 23.10.2012

Citation: Igor Menshov, Alexander Mischenko, Alexey Serejkin, “Numerical modeling elasto-plastic flows by using a Godunov method with moving Eulerian grids”, Matem. Mod., 25:8 (2013), 89–108; Math. Models Comput. Simul., 6:2 (2014), 127–141

Citation in format AMSBIB
\Bibitem{MenMisSer13}
\by Igor~Menshov, Alexander~Mischenko, Alexey~Serejkin
\paper Numerical modeling elasto-plastic flows by using a Godunov method with moving Eulerian grids
\jour Matem. Mod.
\yr 2013
\vol 25
\issue 8
\pages 89--108
\mathnet{http://mi.mathnet.ru/mm3412}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3202329}
\transl
\jour Math. Models Comput. Simul.
\yr 2014
\vol 6
\issue 2
\pages 127--141
\crossref{https://doi.org/10.1134/S2070048214020070}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84923989546}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. B. Kiselev, A. V. Mischenko, “Elastoplastic models to describe experimental data on the spallation fracture under impact of plates”, Moscow University Mechanics Bulletin, 70:6 (2015), 135–143  mathnet  crossref  zmath  isi
    2. K. E. Gorodnichev, P. P. Zakharov, S. E. Kuratov, I. S. Menshov, A. A. Serezhkin, “Razvitie vozmuschenii pri udarnom vozdeistvii neodnorodnoi po plotnosti sredy”, Matem. modelirovanie, 29:3 (2017), 95–112  mathnet  elib
    3. M.-Gwak, Y. Lee, K.-h. Kim, H. Cho, S. J. Shin, J. J. Yoh, “All Eulerian method of computing elastic response of explosively pressurised metal tube”, Combust. Theory Model., 21:2 (2017), 293–308  crossref  mathscinet  isi  scopus
    4. Ilnitsky D.K., Gorodnichev K.E., Serezhkin A.A., Kuratov S.E., Inogamov N.A., Gorodnichev E.E., “A Viscosity Effect on Development of Instabilities At the Interface Between Impacted Plates”, Phys. Scr., 94:7 (2019), 074003  crossref  isi
    5. Serezhkin A., Menshov I., “On Solving the Riemann Problem For Non-Conservative Hyperbolic Systems of Partial Differential Equations”, Comput. Fluids, 210 (2020), 104675  crossref  mathscinet  isi  scopus
    6. Jung S., Myong R.S., “A Relaxation Model For Numerical Approximations of the Multidimensional Pressureless Gas Dynamics System”, Comput. Math. Appl., 80:5 (2020), 1073–1083  crossref  mathscinet  isi
    7. Li R., Wang Ya., Yao Ch., “Arobust Riemann Solver For Multiple Hydro-Elastoplastic Solid Mediums”, Adv. Appl. Math. Mech., 12:1, SI (2020), 212–250  crossref  mathscinet  isi  scopus
    8. Chen L., Li R., Yao Ch., “An Approximate Riemann Solver For Fluid-Solid Interaction Problems With Mie-Gruneisen Equations of State”, Commun. Comput. Phys., 27:3 (2020), 861–896  crossref  mathscinet  isi
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