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The next seminar "Actual problems of applied mathematics" will be held on December 4 at 5 pm (UTC+7).
Seminar heads: I. A. Taimanov, S. I. Kabanikhin, A. E. Mironov, M. A. Shishlenin.
Seminar secretary: N. M. Prokhoshin (n.prokhoshin@g.nsu.ru)

Evgenii I. Romenskii (Sobolev Institute of Mathematics SB RAS) will present his talk "Unified thermodynamically consistent continuum model, its application to the problems of continuum mechanics".

Modern interdisciplinary research focused on applications in science and technology requires the creation of new mathematical and computational models and methods for their solution. Traditional approaches to solving multiphysical big-scale problems are based on the use of classical models of a continuous medium and their conjugation, which creates difficulties in the development of solution methods (e. g. the formulation of boundary conditions for interfaces between media with different properties and their numerical implementation).

The report proposes an alternative approach to modeling multiphysical problems, based on the formulation of a unified model of a continuous medium. Such a model based on a unified system of determinative hyperbolic differential equations allows one to describe the behavior of a medium from an elastic to an elastoplastic state, as well as its flow as a viscous fluid. The unified model is mathematically and thermodynamically correct and allows direct application of modern high-precision numerical methods, which allows us to conclude the reliability of the solutions obtained on its basis. With this approach, multiphysicality is taken into account by nonlinear closing relations in the determinative equations, and boundary interactions are controlled by the conservation laws. This greatly simplifies the computational technique for solving the model, since it allows solving problems on rectangular (parallelepiped) grids using "algorithms of diffused boundaries" for boundary interactions.

A generalization of the unified continuum model for the flow of a viscous heat-conducting fluid in the relativistic case will be considered. Extensions of the model for an elastoplastic medium, taking into account continuous fracture, and for the propagation of small-amplitude waves in a saturated porous medium will also be presented.

In order to participate in the seminar, on December 4 after 4:45 pm (UTC+7) you should connect to the Zoom conference via the following link  or manually using the Zoom conference ID 934 7387 9731.

Please pay attention to the following rules for conducting an Internet seminar:

• To prevent the appearance of spambots, please, use your real first and last name 
• Keep your microphone off during the talk
• Should you have any questions, ask them in the chat