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.
25 МАРТА, 13:00 | ВЫСОКОТОЧНЫЕ БИКОМПАКТНЫЕ СХЕМЫ ДЛЯ ЭВОЛЮЦИОННЫХ УРАВНЕНИЙ В ЧАСТНЫХ ПРОИЗВОДНЫХ
Аудитория: B2-3007 Докладчик: Михаил Брагин, к.ф.-м.н., старший научный сотрудник Института прикладной математики им. М.В. Келдыша РАН, доцент кафедры вычислительной физики МФТИ
Bicompact schemes are finite-difference schemes of higher approximation order on a stencil occupying one mesh cell. Schemes of this type utilize additional dependent variables defined on the set of cell vertices or on a set of certain points on edges, faces, and interiors of cells. Minimization of stencil simplifies the formulation of discrete boundary conditions and significantly reduces amplitude and phase errors. High stability of implicit time integration is combined with an efficient implementation using two-point eliminations.
This report surveys the theory and applications of bicompact schemes. Methods for constructing these schemes for hyperbolic and parabolic equations are explained. Properties of stability, monotonicity, dissipation, and dispersion are described. Numerical results for unsteady multidimensional Euler and Navier-Stokes equations are presented. Emphasis is placed on flows involving the interaction of shock waves with vortices or with each other. The problem of shock-capturing computation of detonation waves at large Damköhler numbers and insufficiently fine grid steps is also considered. A comparison is made with finite-volume WENO schemes.
18 МАРТА, 14:00 | ЧИСЛЕННОЕ И ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ ВЛИЯНИЯ ПОВЕРХНОСТНО-АКТИВНЫХ ВЕЩЕСТВ НА ДИНАМИКУ ВАННЫ РАСПЛАВА И ФОРМИРОВАНИЕ ТОПОГРАФИИ ПОВЕРХНОСТИ ПРИ ЛАЗЕРНОМ ПЛАВЛЕНИИ
Аудитория: B2-3007 Докладчик: Даниил Панов, выпускник программы аспирантуры «Математика и Механика», Сколтех
The dissertation develops a comprehensive computational and experimental framework to address the problem of accounting for the influence of surfactant content on the dynamics of molten metal formed under laser radiation. The primary focus is on modeling the hydrodynamics of the melt with predominant thermocapillary convection and on the mechanisms governing surface topography formation after solidification. The framework is built upon a novel multiphase mathematical model that jointly accounts for capillary and thermocapillary effects, as well as thermal expansion of the metal. Additionally, a new correction procedure that improves the accuracy of free-surface position prediction is proposed. To validate the developed approach, original experimental data were obtained on the effect of surface-active element concentration on melt dynamics, and new parameters for evaluating this influence were proposed. Calibrating the surface tension model parameters on a limited dataset, the temperature dependence of surface tension is established and subsequently validated on an extended dataset. Both experimentally obtained and numerically calculated results confirm the decisive role of surface-active substances in melt dynamics and in the formation of surface morphology after solidification.
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.
