Numerical problems of the modeling of natural and industrial processes in the Arctic zone of the Russian Federation

I. B. Petrov

Čebyševskij sbornik, Tome 18 (2017) no. 3, pp. 428-443

Résumé

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].

Détail

Keywords: numerical methods, mechanics of continuous environments, mechanics of ice, seismic exploration, Arctic.