Welcome to the regular seminars on current research topics in computational mechanics!

Presentations are given by invited lecturers from Skoltech as well as from outside to introduce students to current trends and advances in diverse areas of modern fluid and solid mechanics, applied mathematics, computational science, and industrial applications of mechanics. Students have the opportunity to learn from and interact with leading experts in computational mechanics and to enjoy exposure to cutting-edge topics and open problems in the field.

Speaker's report: 50 min.

Q&A: 10-15 min.

Seminars are held in English.

Lead Instructor: Aslan Kasimov, Associate Professor

Contacts: A.Kasimov@skoltech.ru

OCTOBER 29, 2:00 PM | NUMERICAL EXPERIMENT IN TURBULENCE

Location: B2-3006
Speaker: Svetlana Fortova, Dr. Sci., Institute of Computer Aided Design of the RAS, Professor at the Department of Computational Physics, MIPT

Seminar presentation

This lecture presents the main results on numerical modeling of turbulent flows, carried out under the guidance of academician O.M. Belotserkovsky. The lecture discusses several characteristic problems of turbulence theory. Using the example of free-shear spatial turbulence, the leading role of large vortices is shown and the process of the origin and development of the direct energy cascade by A.N. Kolmogorov is investigated. The development of the reverse energy cascade characteristic of vortex flows in two-dimensional turbulence is demonstrated by the example of a problem proposed by A.N. Kolmogorov (Kolmogorov's problem). For Kolmogorov-type flows that occur when the flow is pumped by an external force and the presence of bottom friction, the occurrence of several different flow regimes is shown: laminar, turbulent, and vortex. The following is an analysis of quasi-two-dimensional flows, often occurring in nature, such as cyclones and anticyclones, which occur under the influence of the Coriolis force. In conclusion, a numerical experiment is presented to study the effect of elastic (polymer) turbulence that occurs at very low Reynolds numbers in the presence of a polymer in the flow.

NOVEMBER 26, 2:00 PM | THE EFFECT OF MEMBRANE DIFFUSION POTENTIAL ON LOSSES IN VANADIUM REDOX FLOW BATTERIES

Location: B2-3006
Speaker: Vignesh Kumar, PhD student of Engineering Systems, Skoltech

Membranes in vanadium redox flow batteries are one of its costliest components. Currently used membranes such as Nafion, suffer from crossover of active species due to weak selectivity of the material. In this work we numerically investigate the loss due to diffusion potential across the membrane caused by unequal mobilities of the ions. We comprehensively describe a two dimensional steady state model and evaluate the contribution of membrane diffusion potential, activation overpotential (loss due to chemical kinetics), and ohmic overpotential (loss due to resistance between components of the cell), to the loss in total cell voltage. We further investigate the impact of this diffusion potential on loss in state of charge when charging the battery over a range of load currents and operating temperatures. Finally, we take several cases of kilo-watt class vanadium flow battery stacks to demonstrate the loss in power due to the diffusion potential.

DECEMBER 3, 2:00 PM | HOW DOES HYDRAULIC FRACTURE PAY BACK TO FRACTURE MECHANICS?

Location: B2-3007
Speaker: Gennady Mishuris, Professor of Mathematical Modelling, Institute of Mathematics and Physics, Aberystwyth University (Wales, United Kingdom)

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

DECEMBER 10, 2:00 PM | CHALLENGE AND MYSTERY OF THE OCEANIC SYNOPTIC EDDIES

Location: B2-3007
Speaker: Pavel Berloff, Professor in Applied Mathematics, Department of Mathematics, Imperial College London (UK)

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.