Finite differences

The finite difference method.

For queries about this topic, contact Ian Hawke.

View the calendar of events relating to this topic.

Projects

Advanced modelling for two-phase reacting flow

Edward Richardson (Investigator)

Engine designers want computer programs to help them invent ways to use less fuel and produce less pollution. This research aims to provide an accurate and practical model for the injection and combustion of liquid fuel blends.

Aerofoil noise

Richard Sandberg (Investigator)

High-performance computing is used to identify noise sources on aerofoils.

Computational electromagnetic modelling of 3D photonic structures

Marc Molinari, Darren Bagnall, Simon Cox (Investigators), Asa Asadollahbaik, Elizabeth Hart

Nano-structured materials can provide very specific and often very special optical effects which can be exploited for a large range of optical applications including wavelength filters, LEDs, micro-lasers, HDTV, solar-cell coatings, optical high-Q fibres, diffraction gratings, polarisation devices, optical switches, etc. This research in “Computational Electromagnetic Modelling of 3D Photonic Structures” aims to address the need for accurate and fast three-dimensional modelling, simulation and analysis processes in the photonics industry. A FEM/FDTD software suite will be developed to simulate Maxwell’s field equations and thin-film quantum effects (plasmons) in the visible and near-infrared EM frequency spectrum. The results obtained from running the software on suitable compute clusters will then be compared to the analysis results of experimentally manufactured materials. We will investigate structures occurring in nature such as iridescent butterfly wings, white/black reflecting beetle shells, etc., and aim to optimise artificially designed structures with periodic, quasi-periodic and random configurations.

Development of a novel Navier-Stokes solver (HiPSTAR)

Richard Sandberg (Investigator)

Development of a highly efficient Navier-Stokes solver for HPC.

Development of wide-ranging functionality in ONETEP

Chris-Kriton Skylaris (Investigator), Jacek Dziedzic

ONETEP is at the cutting edge of developments in first principles calculations. However, while the fundamental difficulties of performing accurate first-principles calculations with linear-scaling cost have been solved, only a small core of functionality is currently available in ONETEP which prevents its wide application. In this collaborative project between three Universities, the original developers of ONETEP will lead an ambitious workplan whereby the functionality of the code will be rapidly and significantly enriched.

Gravitational waves from neutron stars

Ian Hawke (Investigator)

Gravitational waves, once detected, will give information about the extremes of space and time. Compact objects such as neutron stars are perfect locations for generating such waves.

High-resolution shock-capturing (HRSC) methods for elastic matter in general relativity

Carsten Gundlach, Ian Hawke (Investigators)

We are designing HRSC methods for numerical simulation of elastic matter coupled to general relativity and later magnetic fields, with the ultimate aim of simulating old neutron stars, which have elastic crusts.

Is fine-scale turbulence universal?

Richard Sandberg (Investigator)

Complementary numerical simulations and experiments of various canonical flows will try to answer the question whether fine-scale turbulence is universal.

Jet noise

Richard Sandberg (Investigator), Neil Sandham

Direct numerical simulations are used to investigate jet noise.

Laminar to Turbulent Transition in Hypersonic Flows

Neil Sandham, Heinrich Luedeke

Understanding of laminar to turbulent transition in hypersonic boundary-layer flows is crucial for re-entry vehicle design and optimization. The boundary-layer state directly affects the temperatures on the vehicle surface and its viscous drag. Therefore transition has to be considered to correctly compensate for drag and to properly design the thermal protection system.
For the proposed study, in order to obtain a clear understanding of the transition process, the configuration is kept as simple as possible by varying only a minimum number of parameters affecting transition on a simple test geometry such as a swept ramp at different sweep angles. To investigate the influence of such sweep angles on the transition process in the hypersonic regime, Direct Numerical Simulations (DNS) of the turbulent flow field are carried out on the Iridis cluster.

Mathematical modelling of plant nutrient uptake

Tiina Roose (Investigator)

In this project I will describe a model of plant water and nutrient uptake and how to translate this model and experimental data from the single root scale to the root branching structure scale.

Miscible multiphase systems with phase transition

Andrea Boghi

We aim to develop the computational model for the miscible displacement of liquid occupying a porous bulk, as, for instance, in the processes of vegetable solvent extraction, soil remediation or enhanced oil recovery. All these process includes the dissolution of solute and the displacement of solution from porous media. The focus of our current research work is, therefore, twofold: (i) to develop and verify a theoretical model for an evolving miscible displacement, by taking into account dynamic surface tension and mass diffusion through the interphase boundary, and (ii) to provide a model for the solute/solvent displacement from the porous volume.

Modelling micromagnetism at elevated temperature

Hans Fangohr (Investigator), Dmitri Chernyshenko

The project aim is to develop a multiscale multiphysics model of
micromagnetism at elevated temperatures combining finite
element/finite difference modelling with atomistic simulations for
material parameter. The tool will be used to guide the development of the next generation magnetic data storage technology: heat assisted magnetic recording.

Nmag finite difference

Hans Fangohr (Investigator), Dmitri Chernyshenko, Matteo Franchin, Massoud Najafi

The goal of this project is to extends the finite element based micromagnetic simulation tool Nmag by the finite difference based extension Nmagfd and so to get an simulation tool where the user can easily switch between the used discretization method.

Nonlinear Optics in Structured Material

Peter Horak, Neil Broderick (Investigators)

Structured materials such as photonic crystals, optical fibres, Bragg gratings etc. are the ideal material for nonlinear optics. Properly engineered materials allows one to control which nonlinear interactions are observed and enhanced whilst other nonlinear interactions can be neglected. This work looks both at fundamental ideas as well as the fabrication of devices for advanced telecommunications.

Real-time CFD for helicopter flight simulation

Kenji Takeda (Investigator), James Kenny

Project aims to show how real-time computational fluid dynamics (CFD) could be used to improve the realism of helicopter flight simulators.

Self-Force and Black Hole Inspirals

Sam Dolan (Investigator)

We use IRIDIS to compute the self-force acting on a solar-mass black hole orbiting a supermassive black hole.

Soft x-ray science on a tabletop

Peter Horak, Jeremy Frey, Bill Brocklesby (Investigators), Patrick Anderson

Complex numerical simulations are being performed to aid experimentalists at Southampton realize the next generation of high brightness tabletop sources of coherent soft x-rays. 

Stochastic computational methods for aero-acoustics

Gwenael Gabard (Investigator), Martina Dieste

Stochastic methods are used to synthesize a turbulent flow which is then used to model the sound radiated by an airfoil interacting with this turbulence. This approach is faster than performing a complete simulation of the flow field.

Stratified combustion physics and modelling

Edward Richardson (Investigator)

Full-resolution simulation data for turbulent combustion are used to investigate the fundamental impact, and practical modelling, of fuel-air stratification.

Study of global instability in separated flows at high Mach number

Neil Sandham, Zhiwei Hu (Investigators), Kangping Zhang

Flow instability is observed when extending two-dimensional (2D) stable flow into three-dimensional (3D). Development of instability varies along different spanwise length. Thresholds are also discovered for the flow studied to become instable.

Supersonic axisymmetric wakes

Richard Sandberg (Investigator)

Direct numerical simulations are used to shed more light on structure formation and evolution in supersonic wakes.

The effect of roughness upon turbulent supersonic flows

Neil Sandham (Investigator), Christopher Tyson

Understanding the interaction between surface roughness and supersonic air flows are crucial in the design of re-entry vehicles such as the space shuttle. Numerical simulations of these flows has been conducted in order to examine the relationship in order to attempt to achieve a much clearer understanding of the behaviour.

Transition to turbulence in high-speed boundary layers

Neil Sandham (Investigator), Nicola De Tullio

This work is focused on the numerical simulation of hypersonic transition to turbulence in boundary layers. We use direct numerical simulations of the Navier-Stokes equations to analyse the effects of different flow conditions and external disturbances on the transition process. The main objective is to gain insight into the different aspects of transition to turbulence at high speeds, which can lead to the design of new transition models and transition control techniques for high-speed flows.

Whisky Code

Ian Hawke (Investigator)

A 3D finite volume code for simulating compact relativistic hydrodynamics.

µ-VIS Computed Tomography Centre

Ian Sinclair, Richard Boardman, Dmitry Grinev, Philipp Thurner, Simon Cox, Jeremy Frey, Mark Spearing, Kenji Takeda (Investigators)

A dedicated centre for computed tomography (CT) at Southampton, providing complete support for 3D imaging science, serving Engineering, Biomedical, Environmental and Archaeological Sciences. The centre encompasses five complementary scanning systems supporting resolutions down to 200nm and imaging volumes in excess of one metre: from a matchstick to a tree trunk, from an ant's wing to a gas turbine blade.