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.
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
This publication is cited in the following 9 articles:
D. S. Boykov, O. G. Olkhovskaya, V. A. Gasilov, “Coupled simulation of gasdynamic and elastoplastic phenomena in a material under the action of an intensive energy flux”, Math. Models Comput. Simul., 14:4 (2022), 599–612
V. A. Gasilov, A. S. Grushin, A. S. Ermakov, O. G. Olkhovskaya, I. B. Petrov, “Modelling of the destruction of polymers under high energy impact”, Math. Models Comput. Simul., 11:2 (2019), 198–208
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
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
M. A. Zaitsev, S. A. Karabasov, “Skhema Kabare dlya chislennogo resheniya zadach deformirovaniya uprugoplasticheskikh tel”, Matem. modelirovanie, 29:11 (2017), 53–70
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
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
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
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
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