Geodesic
Numerical problems of the modeling of natural and industrial processes in the Arctic zone of the Russian Federation
Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 428-443.

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In this work questions of numerical modeling of dynamic problems of the Arctic zone on high-performance computing systems are considered. The physical sizes of field of integration in such tasks can reach tens and hundreds of kilometers. For correct modeling of distribution wave indignations on such distances are required high-precision numerical methods taking into account wave properties of the solvable equations and also a possibility of modeling of difficult dynamic processes in non-uniform geological environments with a set of contact and free borders. As such numerical method in work the net and characteristic method [1] to the numerical solution of systems of the equations of mechanics of a deformable solid body is used. This method allows to use monotonous differential schemes of the raised order of accuracy [2], to build correct numerical algorithms on borders of fields of integration and on contact borders [3]. This method was already applied to some problems of seismicity in a two-dimensional case [4], in this work modeling was carried out in three-dimensional statement. We will mark that the grid and characteristic method was successfully tested for the numerical decision of tasks in such fields of applied science as hydroaerodynamics, dynamics of plasma, the mechanic of a deformable solid body and corrupting, computing medicine. Examples of its application are described in different appendices in operation [1].
Keywords: numerical methods, mechanics of continuous environments, mechanics of ice, seismic exploration, Arctic. 
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I. B. Petrov. Numerical problems of the modeling of natural and industrial processes in the Arctic zone of the Russian Federation. Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 428-443. http://geodesic.mathdoc.fr/item/CHEB_2017_18_3_a25/

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[4] Kvasov I.E., Pankratov S.A., Petrov I.B., “Computation modeling of seismic response in multilayered geologic medium by grid-characteristic method”, Matematicheskoe modelirovenie, 22:9 (2010), 13–21

[5] MPI Forum. Messagep assing Interface (MPI) Forum Page, , 2009 http://www.mpi-forum.org/

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[7] Ami Harten, “High resolution schemes for hyperbolic conservation laws”, J. of Comp. Phys., 135 (1997), 260–278 | DOI | MR | Zbl

[8] Petrov I.B., Khokhlov N.I., “Comparison of TVD limiters for the numerical solution of the equations of dynamics of a deformable solid body by grid-characteristic method”, Sb. Trudov MFTI Matematicheskie modeli i zadachi upravleniya, 2011, 104–111

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[10] Sannikov A.V., Miryha V.A., Petrov I.B., “Numerical investigation of ice mechanical propaties experiments”, Proc. 3th Int. Scien. Conf. “Polar mechanics” (Vladivostok, 2016), 2016, 14–50

[11] Birykov V.A., Miryaha V.A., Petrov I.B., “Analysis of the Dependence of the Global Load on the Mechanical Parameters of Ice under Interaction between an Ice Field and Construction”, Doclady Academii Nauk, 474:6 (2017), 1–4

[12] Petrov D. I., Petrov I. B., Favorskaya A. V., Khokhlov N. I., “Grid-Characteristic Method on Embedded Hierarchical Grids and Its Application in the Study of Seismic Waves”, Zhurnal vychislitelnoi matematiki i matematicheskoy phisiki, 56:6 (2016), 1149–1163 | DOI | Zbl

[13] Levyant V.B., Petrov I.B., Kvasov I.E., “Numerical modeling of wave response of subvertical crecs”, Technologii seismorazvedki, 2011, no. 4, 41–61

[14] Kvasov I.E., Pankratov S.A., Petrov I.B., “Numerical investigation of dynamic processes in solid with creck by grid-characteristic method”, Matematicheskoe modelirovenie, 22:9 (2010), 13–22

[15] Muratov M.V., Petrov I.B., Sannikov A.V., Favorskaya A.V., “Grid-Characteristic method on nonstructure tetrahedral grids”, Zhurnal vychislitelnoi matematiki i matematicheskoy phisiki, 54:5 (2014), 85–96 | DOI