## Algorithms for computational multiphysics

The Laboratory is developing new mathematical models describing the physics of complex systems and building new algorithms for their numerical solution. An integral part of this work is the development of algorithms which allow for communication between different materials and states of matter at interfaces, as well constructing equations of state for each material and state of matter.

## Supercritical Geothermal Energy Recovery

The Laboratory is working with Quaise Energy on their quest to unlock supercritical geothermal energy for clean electricity generation. Research is on building new mathematical models and algorithms for the numerical simulation of the near- and far-field effects of the ablation of geological materials by means of millimetre wave high-energy beams.

## Magnetic confinement fusion

Magnetic confinement fusion in tokamak reactors is one of the main approaches assessed by government organisations and industry for clean and sustainable energy generation. The Laboratory is developing a computational multiphysics approach for integrated simulations of the complete plasma field inside tokamak reactors and its electromagnetic interaction with the coils, divertor, and the first vessel wall. Initial work is on the development of explicit and all-Mach number algorithms for plasma disruption physics and the mathematical and computational assimilation of plasma boundary physics.

## Lightning Strike on aerospace composites

This research is on the response of aerospace materials interacting with a plasma arc. We have developed novel mathematical models and algorithms to solve the magnetohydrodynamic and the elastoplastic systems of equations simultaneously and evolve the magnetic and electric fields dynamically. The model captures the topological evolution of the arc attachment point and the structural response and Joule heating of the substrate.

## Full-field sonic boom prediction

We have developed a full-field direct numerical simulation methodology for sonic boom in a stratified atmosphere. The entire flow field (from the supersonic body to the ground), is modelled using adaptive mesh refinement to bridge the disparate length scales, a Cartesian cut cell mesh generation for the supersonic body, and a well-balanced finite volume MUSCL-Hancock scheme. The research has been extended to include three-dimensional buildings on the ground.

## MHD Hypersonic Flow Control

Weakly ionised plasmas, formed in high enthalpy hypersonic flows, can be actively manipulated via imposed magnetic fields (magnetohydrodynamic flow control). The technology can replace mechanical control surfaces with magnetic actuation. We have developed a numerical algorithm for the solution of the compressible unsteady Navier-Stokes equations around complex geometries, combined with Maxwell’s equations and closed by a 19-species equation of state for air plasma. Results indicate topological equivalence between the magnetic interaction effects and a generalised mechanical control surface.

## Condensed phase combustion

A computational multiphysics methodology has been developed for the numerical simulation of interacting processes described by a combination of the compressible reactive multiphase Euler equations and elastoplastic equations. These are solved simultaneously by recasting them in the same mathematical form and solving them on the same grid. The communication between the hydrodynamic and elastoplastic systems is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems. The methodology has been used extensively to study the behaviour of condensed phase explosives and the structural response of materials due to detonation propagation.

## Non-Newtonian Flows

Non-Newtonian fluids possess a variety of characteristics which are not well understood. Many of these characteristics originate from local microscopic interactions in the fluid, particularly in complex fluids containing particle or polymer molecule additives. We have developed numerical methodologies for particle-resolved and bulk non-Newtonian flow simulations with complex boundaries. Studies using these algorithms reveal how the interactions between the suspended material, the suspension fluid, and the domain boundaries give rise to non-Newtonian characteristics of the bulk fluid.

## Ultrasonic Excitation of Substrates

Experiments indicate that the ultrasonic excitation of aerospace substrates can prevent ice formation on aircraft wings during flight, but the underlying physics are not understood. We studied the phenomenon by means of a computational multiphysics approach where the equations for the gas, water and solid were solved simultaneously. Results suggest that a cavitation-induced lift-off of the droplet from the surface could account for reducing the thermal contact of the droplet with the substrate, thus preventing it from freezing. This phenomenon has implications for developing more energy-efficient anti-icing technologies than current approaches.

## Additive Manufacturing

Additive manufacturing through selective laser melting of metal powders can print large aircraft parts. The nature of the process may result in porosity and stress-distortion of the printed part. Numerical simulations can help us understand and improve the process. We have developed a thermal modelling approach implemented in an adaptive mesh refinement framework, which can resolve the laser beam effects in a large workpiece lengthscale. The model was validated against experimental results considering a laser spot moving across a solid Ti6Al4V substrate. The model is suitable for parameter studies to assess potential build configurations, and to predict off-design behaviour in complex regions of geometry.

## Numerical relativity

High-resolution shock-capturing schemes have been implemented on curvilinear grids in the context of general relativistic hydrodynamics. These were employed to study Bondi-Hoyle-Lyttleton accretion onto a black hole for ultra-relativistic flows. It is demonstrated that there is quantitative dependence of the shock-angle and mass accretion rate on black hole spin, upstream fluid velocity, and density perturbations. Qualitative dependence of the accretion region and flow features on the same parameters is also shown.

## Global atmospheric chemistry and transport

A three-dimensional mesh-adaptive chemistry and transport model has been developed which is based on a uniform longitude–latitude–height grid. The model is validated using a series of idealised case studies that have exact solutions, and it is then forced by data from meteorological analyses, suitable to study the evolution of trace chemical species in the atmosphere. The model has been employed to study stratosphere-troposphere exchange events and polar stratospheric vortex events.