Title: A stable and dual consistent finite difference method
Date: Monday 2nd October, 2pm, (SCI 0.31)
Speaker: Dr Sofia Eriksson (TU Darmstadt)
Abstract: We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order summation by parts operators, combined with a boundary procedure using penalties (SBP-SAT). Recently it was shown that SBP-SAT finite difference methods can yield super-convergent functional output if the boundary conditions are imposed such that the discretisation is dual consistent. We generalise these results so that they include a broader range of boundary conditions and penalty parameters. The results are also generalised to hold for narrow-stencil second derivative operators. The derivations are supported by numerical experiments.
Title: Chemical front propagation in periodic flows: the role of large deviations
Date: Monday 9th October, 2pm, (SCI 0.31)
Speaker: Dr Alexandra Tzella (University of Birmingham)
Abstract: We discuss the propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) type models in the presence of a steady cellular flow. In the long-time limit, a pulsating front is established. Its speed, on which we focus, can be obtained by solving an eigenvalue problem closely related to large-deviation theory. We employ asymptotic methods to solve this eigenvalue problem in the limit of small molecular diffusivity (large Peclet number, Pe) and arbitrary reaction rate (arbitrary Damkohler number, Da). We identify three regimes corresponding to the distinguished limits Da = O(1/Pe), Da = O(1/logPe) and Da = O(Pe) and, in each regime, obtain the front speed in terms of a different non-trivial function of the relevant combination of Pe and Da, determined by solving a (Pe-independent) one-dimensional problem. Our results are contrasted against front speed values obtained from the so-called G equation: a level-set approximation that is commonly used when Da = O(Pe).
(Joint work with J. Vanneste, Edinburgh).
Title: Acoustic-gravity waves, theory & applications
Date: Monday 16th October, 2pm (SCI 0.31)
Speaker: Dr Usama Kadri (Cardiff University)
Abstract: Acoustic–gravity waves (AGWs) are compression-type waves generated as a response to a sudden change in the water pressure, e.g. due to nonlinear interaction of surface waves, submarine earthquakes, landslides, falling meteorites and objects impacting the sea surface. AGWs can travel at near the speed of sound in water (ca. 1500 m/s), but can also penetrate through the sea-floor surface amplifying their speed, which turns them into excellent precursors. “Acoustic–gravity waves” is an emerging field that is rapidly gaining popularity among the scientific community, as it finds broad utility in physical oceanography, marine biology, geophysics, water engineering, and quantum analogues. This talk is an overview on AGWs, with emphasis on the propagation under elastic ice sheets.
Title: Modulation of multiphase wavetrains and nonlinear reductions
Date: Monday 23rd October, 2pm, (SCI 0.31)
Speaker: Dr Daniel Ratliff (Loughborough University)
Abstract: The modulation of single phase wavetrains (and more recently their generalisation, relative equilibria), instigated by Whitham, is a field that has been developed over the last 50 years. The procedure generates a set of dispersionless nonlinear PDEs that govern the local wavenumber and frequency of the wave. When these degenerate, it has been shown that dispersion emerges at such points leading to equations such as the Korteweg-de Vries (KdV) equation. Remarkably, such reductions possess coefficients that may be related to the conservation laws of the original system which can be calculated in advance. This property is known as ‘universal form’.
This talk concerns itself with taking these ideas and applying them to solutions that have more than one phase. The questions are now this – which nonlinear PDEs arise? Do these nonlinear reductions still emerge with universal form? It will be shown that yes, these properties generalise quite nicely to the multiphase problem and recover many of the same equations derived from single phased solutions (like the KdV). Unsurprisingly, the increase in the number of system parameters allows one to derive further nonlinear PDEs (and even some new ones).
The talk concludes (hopefully, time permitting) by discussing two applications of the theory. The first is a stratified shallow water system and the second is a set of coupled Nonlinear Schrodinger equations (which model ocean wave envelopes, Bose-Einstein condensates and electromagnetic waves), showing the possible reductions and how the conditions for each equation can be met.
This work is in collaboration with Tom Bridges (University of Surrey).
Title: How to make a splash: from high speed droplet impact to a novel methodology for calculating water catch on aircraft surfaces
Date: Monday 6th November, 2pm, (SCI 0.31)
Speaker: Dr Radu Cimpeanu (University of Oxford)
Abstract: A new methodology for the calculation of water collection efficiency on aircraft surfaces is discussed. The approach incorporates the detailed fluid dynamical processes often ignored in this setting, such as the drop interaction with the surrounding air flow, drop deformation, rupture and coalescence, as well as the motion of the ejected microdrops in the computational domain. Direct numerical simulations using the volume-of-fluid technique are performed using modelling assumptions which enable us to take advantage of the disparity of lengthscales in the system. Comparisons are performed in the pre-impact regime with available experimental data, while the early stages of the impact are validated using the analytical framework provided by Wagner theory, context in which recent developments are also presented. We then focus on quantifying useful information on the liquid movement on longer timescales. The analysis shows a high degree of flexibility and can be used efficiently when considering changes in geometry (aircraft design), flow conditions and cloud characteristics. The interaction with our industrial partners will also be a point of focus, in particular in the context of developing a framework that incorporates the above analysis in an industrial work pipeline with no additional computational cost, thus making direct use of several hundreds of thousands of hours of CPU time on local supercomputing facilities. The methodology is finally applied to representative test geometries in collaboration with our partners.
Title: Multilayer networks: a new framework for complex systems
Date: Monday 20th November, 2pm, (SCI 0.31)
Speaker: Dr Ginestra Bianconi (Queen Mary University London)
Abstract: Multilayer networks describe interacting complex systems formed by different interacting networks. Multilayer networks are ubiquitous and include social networks, financial markets, multimodal transportation systems, infrastructures, the brain and the cell. Multilayer networks cannot be reduced to a large single network. In this talk I will present first recent results showing how we can extract from multilayer networks more relevant information than from its single layer taken in isolation. Secondly I will provide evidence that dynamical processes on multilayer networks can display very novel properties that reflect the rich interplay between structure and multiplexity.
Title: When is the effective wavefield a useful tool to predict wave attenuation over long distances?
Date: Monday 27th November, 2pm, (SCI 0.31)
Speaker: Dr Luke Bennetts (University of Adelaide)
Abstract: Anderson localisation theory tells us that waves attenuate through disordered media, and this talk is motivated by seeking efficient ways to calculate the attenuation rate as a function of the incident wave properties (frequency) and properties of the given medium, including the statistical properties of the disorder. Effective media theory is an appealing way to approach the problem, as it provides analytical insight, circumventing the need to repeatedly compute individual wave fields for different realisations of the disorder, as well providing the opportunity for elegant mathematical analysis. I will discuss the usefulness of effective media theory in the setting of two canonical, linear 1D problems, along the way outlining some associated effective media methods. The findings are in some respects entirely intuitive, but in other respects surprising.
Title: Feedback control of thin film flows
Date: Monday 4th December, 2pm, (SCI 0.31)
Speaker: Dr Susana Gomes (Imperial College London)
Abstract: The flow of a thin film down an inclined plane is unstable when the Reynolds number is larger than a critical value depending on the slope angle. These flows are important for many industrial applications, including coating and heat transfer. While some applications benefit from a flat film, in many cases one wishes to explore the flow’s instabilities and drive the system towards a non-uniform state.
In this talk, I will present a control methodology based on same-fluid blowing and suction at the wall. Given a desired interface shape, we apply controls which are proportional to the deviation between the current state of the system and the chosen solution. We study the effect of these controls on three partial differential equations which model the interfaces of thin film flows in different limits: two long-wave models (the Benney equation and a first-order weighted residuals model) and in the weakly nonlinear regime (the Kuramoto-Sivashinsky (KS) equation). We show that for the KS equation we can use a finite number of point-actuated controls based on observations of the full interface to stabilise both the flat solution and chosen nontrivial solutions, and investigate the robustness of the designed controls to uncertain observations and/or parameter values. Furthermore, we show robustness of the controls between the more general models and to limited observations.
Title: The terminal motion of sliding spinning disks with uniform Coulomb friction
Date: Wednesday 6th December, 2pm, (Queens 2.21)
Speaker: Prof Patrick Weidman (University of Colarado Boulder)
Abstract: We review the classical paper by Farkas et al. (2003) concerning the motion of a disk of radius R sliding and spinning with uniform dry friction across a horizontal plane showing that sliding and spinning stop at the same instant. Moreover, under arbitrary nonzero initial values of translational speed v and angular rotation rate omega, the terminal value of the speed ratio epsilon_0 = v/(omega*R) is always 0.653. In the current study we extend these results to annular disks and two-tier disks. It is found that an annular disk of radius ratio eta = R1/R2 stops sliding and spinning at the same time, but with a terminal speed ratio epsilon_0 dependent on eta. For a two-tier disk with lower tier of thickness H1 and radius R1 and upper tier of thickness H2 and radius R2, the motion depends on both eta and the thickness ratio lambda = H1/H2. However, these can be combined into a single parameter k, the normalized radius of gyration: when k > 2/3 sliding stops first and the disk spins to rest; when 1/2 < k < 2/3 sliding and spinning stop at the same time; and when k < 1/2 rotation stops first and the disk slides to rest. Experiments performed with PVC disks moving on a nylon fabric stretched over a horizontal table corroborate fairly well the three different types of terminal motions.
Date: Monday 11th December, 2pm, (SCI 0.31)
Speaker: Prof Onno Bokhove (University of Leeds)