# Preprints

Filtering by Subject: Numerical Analysis and Computation

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

**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

**Published**: 2020-05-25

**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

**Published**: 2020-04-13

**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

**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

**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

**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 [...]

## Certified Reduced Basis Method in Geosciences Addressing the challenge of high dimensional problems

**Published**: 2019-06-28

**Subjects**: Applied Mathematics, Earth Sciences, Numerical Analysis and Computation, Partial Differential Equations, Physical Sciences and Mathematics

One of the biggest challenges in Computational Geosciences is finding ways of efficiently simulating high-dimensional problems. In this paper, we demonstrate how the RB method can be gainfully exploited to solve problems in the Geosciences. The reduced basis method constructs low-dimensional approximations to (high-dimensional) solutions of parametrized partial differential equations. In contrast [...]

## Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

**Published**: 2017-11-21

**Subjects**: Applied Mathematics, Computer Sciences, Earth Sciences, Fluid Dynamics, Geophysics and Seismology, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Physical Sciences and Mathematics, Physics

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. Crucially, in this formulation the effective or eddy diffusivity depends on the entropy gradient, dS/dr, as well as entropy itself. First we present a simplified model with [...]

## Basis functions for the consistent and accurate representation of surface mass loading

**Published**: 2017-11-13

**Subjects**: Applied Mathematics, Earth Sciences, Environmental Indicators and Impact Assessment, Environmental Monitoring, Environmental Sciences, Geophysics and Seismology, Numerical Analysis and Computation, Oceanography and Atmospheric Sciences and Meteorology, Other Earth Sciences, Other Environmental Sciences, Other Oceanography and Atmospheric Sciences and Meteorology, Other Physical Sciences and Mathematics, Physical Sciences and Mathematics

Inversion of geodetic site displacement data to infer surface mass loads has previously been demonstrated using a spherical harmonic representation of the load. This method suffers from the continent-rich, ocean-poor distribution of the geodetic data, coupled with the predominance of the continental load (water storage and atmospheric pressure) compared with the ocean bottom pressure (including [...]

## Computationally Efficient Tsunami Modelling on Graphics Processing Units (GPU)

**Published**: 2017-11-13

**Subjects**: Applied Mathematics, Civil and Environmental Engineering, Civil Engineering, Computer Sciences, Earth Sciences, Engineering, Environmental Sciences, Geophysics and Seismology, Hydraulic Engineering, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Other Civil and Environmental Engineering, Other Earth Sciences, Other Environmental Sciences, Physical Sciences and Mathematics

Tsunamis generated by earthquakes commonly propagate as long waves in the deep ocean and develop into sharp-fronted surges moving rapidly towards the coast in shallow water, which may be effectively simulated by hydrodynamic models solving the nonlinear shallow water equations (SWEs). However, most of the existing tsunami models suffer from long simulation time for large-scale real-world [...]