The many small inhabited islands of the Sundabarn region in north east India and Bangladesh, are subject to sea water flooding during cyclones. The objective is to predict flood risk so that improvements to flood defences can be prioritised. There are a few records of flood heights at a very limited set of locations, but there are long term data on cyclones that can be used to drive a simulation model to estimate flood risk at any points in the Sundarbans. The cyclone data is used to fit a stochastic model for cyclones. The cyclone model is combined with a deterministic storm surge model that provides sea level at the boundary of the Sundarbans. A hydraulic routing model, MIKE–21, is then used to predict water levels over a grid of interior points. The combined deterministic surge and routing models are approximated by a regression type model, so the stochastic simulation can quickly generate thousand of years of flood events. Results from a simulation are presented.

The problem of laminar flow in a rectangular channel with a pair of porous walls is considered. The porous walls allow fluid to be injected into or sucked out of the channel at constant velocities normal to the walls; the velocities at each wall are not necessarily of equal magnitude nor symmetrical in direction. In this article, a unique solution to this problem is shown to exist for sufficiently low Reynolds numbers through the application of Banach's fixed point theorem. This serves to further the discussion about the uniqueness of solutions for this problem, whilst also demonstrating the suitability of a fixed point approach to this family of fluid dynamics problems.

Compared to more typical computational fluid dynamics techniques, the lattice Boltzmann method (LBM) is relatively new and unexplored. In recent years, axisymmetric LBM formulations, which can simulate flow in rotationally symmetric 3D geometries, have been published. Here we verify a novel axisymmetric LBM implementation using numerical criteria. Hagen–Poiseuille and Womersley flow are considered within a straight tube where analytic solutions are available. With this, we establish sufficient accuracy of the approximated flow and study the effects of changing simulation parameters (e.g. Reynolds number, Womersley number) and spatial/temporal parameters (e.g. relaxation time, mesh nodes, time steps). Furthermore, steady and oscillatory flows within a periodically-varying, longitudinally asymmetric geometry are considered. Analytic solutions are not available in these cases; however, the validity of the axisymmetric LBM for curved boundaries is ensured through convergence, mesh independence and qualitative observations. Guaranteeing reasonable flow field determination for the aformentioned geometry is relevant to a larger problem where particulate suspension is pumped back and forth through a membrane of axisymmetric micropores. In these circumstances, experiments have induced directed particle transport even though there is no net flow of the carrier fluid. Hence, our work aims to improve current numerical simulations of these flow problems to better understand the factors that facilitate particle transport.

The Concurrent Reduced Memory Access method (CRMA) is a scalable memory-efficient Monte Carlo method for computing the lineal path function. It addresses an inherent memory bottleneck of lineal path function algorithms by utilising known properties of the two-point correlation function to reduce the number of voxels where the phase value must be evaluated. The CRMA method reduces the computation time and improves the scalability characteristics of the traditional lineal path function Monte Carlo methods. CRMA also provides additional information useful for analysing microstructures since the two-point correlation function is computed as part of the method. The CRMA method offers an efficient, scalable and extendable solution for computing the lineal path function.

We present a new initialisation of an adaptive batch strategy to compute the ε-approximate minimum volume covering ellipsoid (MVCE) for a set of n points. We focus on moderately sized datasets (up to dimension d = 100 and n = 1 000 000). The adaptive batch strategy works in an optimisation-deletion-adaptation cycle: we solve the MVCE problem using a smaller number of points, we delete points from consideration that are guaranteed to not lie on the boundary of the MVCE, and then carefully select a new batch of points. We propose a new initialisation, which involves selecting the points corresponding to some highest leverage scores. We show using numerical examples that this new initialisation tends to improve computation time as well as reduce the total number of cycles, as compared with initialising with a random selection of points.

Modern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately simulate over large scales through computations on only small well-separated patches of the microscale system. Here the microscale system is a solid beam of random heterogeneous elasticity. The continuing challenge is to compute the given physics on just the microscale patches, and couple the patches across un-simulated macroscale space, in order to establish efficiency, accuracy, consistency, and stability on the macroscale. Dynamical systems theory supports the scheme. This research program is to develop a systematic non-intrusive approach, both computationally and analytically proven, to model and compute accurately macroscale system levels of general complex physical and engineering systems.

Metallurgical coke is a crucial component in the production of steel worldwide. It is a porous composite material, created by conversion of metallurgical coal in a coke oven. A key property of metallurgical coke is its strength, and there is evidence that poor interface quality between the two key components of coke can have deleterious effect on coke strength. Here we create small samples of coke and image them using high resolution 3D micro-CT, with pixel size of approximately \(8\,\mu\)m. We use a Gabor filter, combined with morphology techniques to isolate the different components in the samples. We then develop a measure, called excess porosity to quantify the quality of the interfaces between components. This measure enables us to highlight problem interactions between components.

We present a method for recovering the Hessian from a linear finite element approach to achieve a higher rate of convergence. This method uses an \(L^{2}\)-based projection as well as boundary modification to achieve and improve the convergence rate. The projection uses a biorthogonal system to make the computation more numerically efficient. We present numerical examples to illustrate the efficiency and optimality of our approach on different meshes. The performance of our approach on adaptively refined meshes is briefly explored.

A highly accurate and efficient method to compute the expected values of the count, sum, and squared norm of the sum of the centre vectors of a random maximal sized collection of non-overlapping unit diameter disks touching a fixed unit-diameter disk is presented. This extends earlier work on Renyi's parking problem [Magyar Tud. Akad. Mat. Kutato Int. Kozl. 3 (1–2), 1958, pp. 109–127]. Underlying the method is a splitting of the the problem conditional on the value of the first disk. This splitting is proven and then used to derive integral equations for the expectations. These equations take a lower block triangular form. They are solved using substitution and approximation of the integrals to very high accuracy using a polynomial approximation within the blocks.

We present an efficient data-driven offline/online Bayesian algorithm for uncertainty quantification (UQ) in the induced scattered field when a time-harmonic incident wave interacts with an uncertain heterogeneous medium. The incident wave of interest need not be known in advance, and the uncertainty is informed by noisy scattering data obtained from other incident waves impinging on the medium. Our UQ algorithm is accelerated by a novel stochastic reduced order model (ROM) based on the T-matrix, and the ROM is independent of both the incident wave, and other incident waves used to generate the data. This important property allows the model to be set up offline.