Добро пожаловать на регулярные семинары по актуальным темам исследований в области вычислительной механики!

Приглашённые лекторы из Сколтеха и других вузов выступают с докладами, чтобы познакомить студентов с текущими исследованиями и достижениями в различных областях современной механики жидкости и твёрдого тела, прикладной математики, вычислительной математики и промышленного применения механики. Студенты получают возможность узнать об актуальных проблемах механики у ведущих специалистов в области вычислительной механики.

Продолжительность доклада: 50 минут

Q&A: 10-15 минут

Семинары проводятся на английском языке.

Ведущий преподаватель: Аслан Касимов, доцент

Контакты: A.Kasimov@skoltech.ru

4 МАРТА, 14:00 | МОДЕЛИРОВАНИЕ ДИНАМИКИ ВЕЧНОЙ МЕРЗЛОТЫ С ИСПОЛЬЗОВАНИЕМ ФИЗИЧЕСКИ-ИНФОРМИРОВАННЫХ НЕЙРОННЫХ СЕТЕЙ

Аудитория: B2-3007
Докладчик: Георгий Фишер, аспирант программы «Нефтегазовое дело», Сколтех

Permafrost degradation under a changing climate poses significant environmental and engineering risks, from infrastructure destabilization to large-scale greenhouse gas emissions. Predicting the thermo-physical behavior of permafrost soils requires solving a Stefan-like heat transfer problem with a moving phase boundary, complicated by heterogeneous and poorly characterized thermal properties that vary with depth, soil composition, and freeze–thaw state. Traditional forward modeling approaches demand detailed knowledge of these properties — thermal conductivity, volumetric heat capacity, latent heat — which are expensive to measure in situ and often unavailable at the required spatial resolution.

In this seminar, we explore the application of Physics-Informed Neural Networks (PINNs) to the permafrost modelling problem, discussing spatially variable thermal properties and the subsurface temperature field predictions from sparse borehole observations. We discuss the key architectural and training challenges specific to this class of problems — including the sensitivity of identified parameters to loss formulation, boundary conditions, and network design — and utilize open field data from an Arctic permafrost monitoring site. The work is situated at the intersection of scientific machine learning, geotechnical engineering, and cryosphere science, and may be of interest to researchers working on data-driven approaches to subsurface characterization, phase-change problems, and climate-driven geohazards.

17 ДЕКАБРЯ, 14:00 | РОСАТОМ - ПРОГРАММНЫЕ ПРОДУКТЫ И ИХ ПРИМЕНЕНИЕ ДЛЯ НАУЧНОГО ИНЖИНИРИНГА

Аудитория: B2-3007
Докладчик: Дмитрий Фомичёв, директор по математическому моделированию, руководитель программ Департамента информационных технологий, ГК Росатом 

The report is dedicated to Russian software products and their application in scientific research and engineering using the example of nuclear industry tasks. The report analyzes in detail key software systems such as the modular supercomputer platform Logos (including its specialized modules “Aero-Hydro”, “Heat”, and “Strength”), the design environment REPEAT used for creating digital twins, as well as New Generation Codes for radiation and environmental modeling. Specific examples demonstrate their use for modeling physical processes, from aerohydrodynamics and heat transfer to strength analysis and evaluation of structures resource.

Examples of end-to-end digital design, disaster scenario analysis, multidisciplinary optimization, and virtual testing will be examined. The presentation provides an overview of promising areas of engineering development, including the integration of machine learning methods such as physically informed neural networks (PINN), the use of reduced dimension models (ROM) and the study of quantum computing potential for engineering problems solving.

10 ДЕКАБРЯ, 14:00 | ВЫЗОВЫ И ЗАГАДКИ СИНОПТИЧЕСКИХ ВИХРЕЙ В ОКЕАНЕ

Аудитория: B2-3007
Докладчик: Проф. Павел Берлов, Специалист по прикладной математике, Факультет математики, Имперский Колледж Лондона (Великобритания)

This talk aims at broader audience and will discuss some most important aspects of the eddies and their dynamics in a way accessible to non-experts. Until the late 1960s, oceanographers thought of the ocean circulation as consisting of nearly laminar (i.e., smooth and steady) currents: slowly moving interior gyres, fast moving western boundary currents, and mighty Antarctic circumpolar current. However, over the years strong evidence emerged that the ocean circulation also contains ubiquitous and vigorous mesoscale (synoptic) eddies characterized by spatial scales from a few kilometers to hundreds of kilometers, evolving over time scales from weeks to years.

Physical oceanographers observe these eddies from the surface-drifter and deep-float trajectories, from satellite images of sea surface height, temperature, and ocean color, from underwater acoustic and current measurements. On the larger scales these eddies are thought of as giant planetary waves, and on the smaller scales they are blended with internal gravity waves, giving rise to various submesoscale phenomena. The eddies populate all parts of the ocean, including the Arctic and Antarctic regions, and they tend to be larger near the equator and smaller towards the poles. The eddies constitute “oceanic weather”, because they are dynamically analogous to atmospheric cyclones and anticyclones in common weather maps. They are viewed as specific turbulence that exists in stratified fluids on surfaces of rotating planets. The eddies are characterised by pressure anomalies associated with spatial changes in water density. The corresponding pressure gradients are nearly exactly balanced by the Coriolis force arising due to the Earth rotation — this is the geostrophic balance, which results in solenoidal flow motions.

The eddies are controlled by large-scale background currents, by bottom topography and continental boundaries, by interactions with the atmosphere, and by variety of physical processes on smaller scales. They are forced by complex instabilities of large-scale currents, which are in turn driven by the atmospheric momentum, heat, and fresh water fluxes. The main reason to care about the eddies has to do with their roles in global climate, because the eddies play crucial role in shaping up oceanic general circulation, which is the most important part of the climate system, along with the atmosphere. The oceanic general circulation plays important role in the present climate by redistributing heat, which is a key player in climate change and sea level rise, and by recycling carbon.

The main eddy roles in ocean circulation and climate are: (1) maintaining large-scale currents through nonlinear turbulent stresses; (2) converting large-scale available potential energy into kinetic energy of nearly horizontal vortical motions; (3) cascading spectral energy to the larger and smaller scales; (4) Lagrangian dispersion of material properties and eddy induction of mean transport; (5) control over stratification and restratification in the upper-ocean mixed layer; (6) ventilation of the interior ocean; (7) eddy-induced frontogenesis; (8) eddy pumping and quenching of nutrients to the euphotic zone; (9) eddy-induced climate variability; and (10) ocean-atmosphere interactions and coupling. Fundamental properties of the eddies are studied within the framework of geophysical fluid dynamics, and practical applications of the outcome are immense.

3 ДЕКАБРЯ, 14:00 | РОЛЬ ГИДРОРАЗРЫВА ПЛАСТА В МЕХАНИКЕ РАЗРУШЕНИЯ

Аудитория: B2-3007
Докладчик: Проф. Геннадий Мишурис, Эксперт по математическому моделированию, Институт математики и физики, Университет Аберистуита, Уэльс, Великобритания 

This talk aims to provide an overview of key results in the mathematical and numerical modelling of hydraulic fracture that my group and I have been privileged to work with over the last decade. Revisiting the approach to a basic (BEM) algorithm for the classic HF models (PKN, KGD, Radial) has eventually allowed us to construct an extremely accurate and effective time-space adaptive algorithm for the models. Utilising this algorithm, and adjusting where necessary, we have been continuing our endeavour to analyse some of the more delicate pieces of this extremely rich theory. In particular, we considered the effect of the shear traction induced by the fluid on the crack surface and discovered another, fourth, stress intensity factor, which to our best knowledge, was not previously known in classical Fracture Mechanics. This required us to compute Rice’s Energy Release Rate, taking the effect into account. Furthermore, discussing the results, we have extended Irwin’s classic crack closure integral representation to the ERR computation. Interestingly, this leads to a complete LEFM theory with six SIFs with applications to, among others, hydraulic fracturing, soft materials containing stiff inclusions, rigid inclusions, shear bands and cracks characterised by the Gurtin-Murdoch surface stress elasticity. It also resolves an ambiguity in using the same SIF’s terminology in the cases of open cracks and rigid inclusions.

The talk requires basic knowledge in the areas of Elasticity, Fracture Mechanics, and numerical simulation. Lengthy derivations will be avoided, reducing mathematical details to an absolute minimum required for understanding, while presenting most of the results in their graphical forms. All details of the reported research can be found in the following papers:

[1] Piccolroaz, A., Peck, D., Wrobel, M., Mishuris, G. (2021). Energy release rate, the crack closure integral and admissible singular fields in Fracture Mechanics, IJES, 164, 103487, 10.1016/j.ijengsci.2021.103487

[2] Wrobel, M., Mishuris, G., Piccolroaz, A. (2017) Energy release rate in hydraulic fracture: Can we neglect the impact of the hydraulically induced shear stress? IJES, 111, 28-51. 10.1016/j.ijengsci.2016.09.013

[3] Wrobel, M. Mishuris, G. (2015) Hydraulic fracture revisited: Particle velocity-based simulation. IJES, 94, 23-58, 10.1016/j.ijengsci.2015.04.003