Preprints

Filtering by Subject: Numerical Analysis and Computation

Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation

Joseph Gregory Wallwork, Athanasios Angeloudis, Nicolas Barral, et al.

Published: 2022-04-30
Subjects: Civil and Environmental Engineering, Fluid Dynamics, Geophysics and Seismology, Numerical Analysis and Computation, Partial Differential Equations

Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation. Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the [...]

A consistent mass-conserving C-staggered method for shallow water equations on global reduced grids

Genilson Schunck de Lima, Pedro da Silva Peixoto

Published: 2022-03-25
Subjects: Numerical Analysis and Computation

The increasing number of cores in modern supercomputers motivated the search for methods with better scalability to model the atmospheric dynamics in global weather forecasting and climate simulations. This objective renewed the interest in grid-point schemes with quasi-uniform spherical grids, with each alternative providing some good properties and some disadvantages. Here, we target reduced [...]

Uncertainty and sensitivity analysis for probabilistic weather and climate risk modelling: an implementation in CLIMADA v.3.1.

Chahan M. Kropf, Alessio Ciullo, Laura Otth, et al.

Published: 2022-02-23
Subjects: Applied Statistics, Climate, Design of Experiments and Sample Surveys, Earth Sciences, Environmental Studies, Natural Resources Management and Policy, Nature and Society Relations, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Risk Analysis, Statistical Methodology

Modelling the risk of natural hazards for society, ecosystems, and the economy is subject to strong uncertainties, even more so in the context of a changing climate, evolving societies, growing economies, and declining ecosystems. Here we present a new feature of the climate risk modelling platform CLIMADA which allows to carry out global uncertainty and sensitivity analysis. CLIMADA underpins [...]

Calibration, inversion and sensitivity analysis for hydro-morphodynamic models

Mariana C A Clare, Stephan C Kramer, Colin J Cotter, et al.

Published: 2021-08-03
Subjects: Applied Mathematics, Fluid Dynamics, Geomorphology, Numerical Analysis and Computation, Partial Differential Equations, Programming Languages and Compilers

The development of reliable, sophisticated hydro-morphodynamic models is essential for protecting the coastal environment against hazards such as flooding and erosion. There exists a high degree of uncertainty associated with the application of these models, in part due to incomplete knowledge of various physical, empirical and numerical closure related parameters in both the hydrodynamic and [...]

Assessing erosion and flood risk in the coastal zone through the application of the multilevel Monte Carlo method

Mariana C A Clare, Matthew Piggott, Colin J Cotter

Published: 2021-01-07
Subjects: Applied Mathematics, Earth Sciences, Geomorphology, Hydrology, Numerical Analysis and Computation, Risk Analysis, Statistics and Probability

The risk from erosion and flooding in the coastal zone has the potential to increase in a changing climate. The development and use of coupled hydro-morphodynamic models is therefore becoming an ever higher priority. However, their use as decision support tools suffers from the high degree of uncertainty associated with them, due to incomplete knowledge as well as natural variability in the [...]

Multi-scale hydro-morphodynamic modelling using mesh movement methods.

Mariana C A Clare, Joseph Gregory Wallwork, Stephan C Kramer, et al.

Published: 2020-10-22
Subjects: Applied Mathematics, Geomorphology, Mathematics, Numerical Analysis and Computation, Partial Differential Equations

Hydro-morphodynamic models are an important tool that can be used in the protection of coastal zones. They can be required to resolve spatial scales ranging from sub-metre to hundreds of kilometres and are computationally expensive. In this work, we apply mesh movement methods to a depth-averaged hydro-morphodynamic model for the first time, in order to tackle both these issues. Mesh movement [...]

Robust Q estimation using surface seismic data

Joakim Oscar Blanch

Published: 2020-07-30
Subjects: Applied Mathematics, Computational Engineering, Earth Sciences, Engineering, Geophysics and Seismology, Numerical Analysis and Computation, Physical Sciences and Mathematics

Direct wave arrivals are the most robust signals to determine velocity and consequently they have been used for almost a century in hydrocarbon exploration. The reason is simple as the arrivaltime is explicitly available and provide a direct measurement of the average velocity of the sub-surface ray-path. These signals have not been extensively used to estimate attenuation or Q. One reason may [...]

Modelling an energetic tidal strait: investigating implications of common numerical configuration choices

Lucas Mackie, Paul Evans, Magnus Harrold, et al.

Published: 2020-07-16
Subjects: Applied Mathematics, Civil and Environmental Engineering, Civil Engineering, Engineering, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Characterising tidal hydrodynamics in the vicinity of submerged features can be demanding given the hostility of the marine environment. Logistical challenges in the measurement of such flows has promoted research on wake studies through physical and numerical modelling. In this study, site measurements and modelled data are combined to provide an insight into the regional hydrodynamics within a [...]

Adjoint-based sensitivity analysis for a numerical storm surge model

Simon Charles Warder, Kevin Horsburgh, Matthew Piggott

Published: 2020-06-29
Subjects: Applied Mathematics, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Numerical storm surge models are essential to forecasting coastal flood hazard and informing the design of coastal defences. However, such models rely on a variety of inputs, many of which will carry uncertainty, and an awareness and understanding of the sensitivity of the model outputs with respect to those uncertain inputs is necessary when interpreting model results. Here, we use an [...]

A comparison of Bayesian inference and gradient-based approaches for friction parameter estimation

Simon Charles Warder, Athanasios Angeloudis, Stephan C. Kramer, et al.

Published: 2020-06-29
Subjects: Applied Mathematics, Numerical Analysis and Computation, Oceanography, Oceanography and Atmospheric Sciences and Meteorology, Physical Sciences and Mathematics

Numerical tidal models are essential to the study of a variety of coastal ocean processes, but typically rely on uncertain inputs, including a bottom friction parameter which can in principle be spatially varying. Here we employ an adjoint-capable numerical ocean model, Thetis, and apply it to the Bristol Channel and Severn Estuary, using a spatially varying Manning coefficient within the bottom [...]

Stress Recovery for the Particle-in-cell Finite Element Method

Haibin Yang, Louis Moresi, John Mansour

Published: 2020-05-26
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geophysics and Seismology, Mathematics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Physical Sciences and Mathematics, Tectonics and Structure

The interelement stress in the Finite Element Method is not continuous in nature, and stress projections from quadrature points to mesh nodes often causes oscillations. The widely used particle-in-cell method cannot avoid this issue and produces worse results when there are mixing materials of large strength (e.g., viscosity in Stokes problems) contrast in one element. The post-processing methods [...]

A mixed $RT_0 - P_0$ Raviart-Thomas finite element implementation of Darcy Equation in GNU Octave

Agah D. Garnadi, Corinna Bahriawati

Published: 2020-04-14
Subjects: Applied Mathematics, Bioresource and Agricultural Engineering, Chemical Engineering, Computational Engineering, Earth Sciences, Engineering, Environmental Sciences, Hydrology, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics, Water Resource Management

In this paper we shall describe mixed formulations -differential and variational- of Darcys flow equation, an important model of elliptic problem. We describe * Galerkin method with finite dimensional spaces; * Local matrices and assembling; * Raviart-Thomas $RT_0 - P_0$ elements; * Edge basis and local matrices for $RT_0 - P_0$ FEM; * Model problem with corresponding local matrices, right hand [...]

Hydro-morphodynamics 2D modelling using a discontinuous Galerkin discretisation

Mariana C A Clare, James Percival, Athanasios Angeloudis, et al.

Published: 2020-01-09
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geomorphology, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics, Sedimentology

The development of morphodynamic models to simulate sediment transport accurately is a challenging process that is becoming ever more important because of our increasing exploitation of the coastal zone, as well as sea-level rise and the potential increase in strength and frequency of storms due to a changing climate. Morphodynamic models are highly complex given the non-linear and coupled nature [...]

Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling

Joseph Gregory Wallwork, Nicolas Barral, Stephan C. Kramer, et al.

Published: 2019-12-31
Subjects: Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics

Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this [...]

Controls on the development and termination of failed continental rifts: Insights from the crustal structure and rifting style of the North Sea via ambient noise tomography

Emily Crowder, Nick Rawlinson, David Cornwell, et al.

Published: 2019-09-21
Subjects: Applied Mathematics, Computer Sciences, Earth Sciences, Geophysics and Seismology, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Physical Sciences and Mathematics, Probability, Statistics and Probability

The mid to lower crust plays an important role in rift initiation and evolution, particularly when large scale sutures and/or terrane boundaries are present. These inherited features can focus strain or act as inhibitors to extensional deformation. Ancient tectonic features are known to exist beneath the iconic failed rift system of the North Sea making it the ideal location to investigate the [...]

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