Numerical Analysis Group (NAG)

Our Numerical Analysis Group develop mathematical models, advanced computational algorithms and high-performance software for the design and analysis of complex systems in engineering via differential equations. Our highly skilled staff help contribute to advances in modelling and simulation based engineering. Current focus of this research group lies in the intersection of federated digital twins, non-linear (black box) optimisation, integration of artificial intelligence for demand forecasting, structural lightweighting and process engineering applications. Our goals are high-performance, multi-scale modelling for the high-fidelity analysis of multi-physics problems, high-order methods, uncertainty quantification, and efficient model-order reduction for large scale applications such as design and active control.

Digital Twin Applications

A digital twin can be defined, fundamentally, as an evolving digital profile of the historical and current behaviour of a physical object or process that helps optimise business performance. The digital twin is based on massive, cumulative, real-time, real-world data measurements across an array of dimensions. These measurements can create an evolving profile of the object or process in the digital world that may provide important insights on system performance, leading to actions in the physical world such as a change in product design or manufacturing process.

The primary focus within NAG is to support and build high fidelity models for federated digital twin applications, ranging from buildings to city level power grids. Until recently, the digital twin—and the massive amounts of data it processes—often remained elusive to enterprises due to limitations in digital technology capabilities as well as prohibitive computing, storage, and bandwidth costs. Such obstacles, however, have diminished dramatically in recent years. Significantly lower costs and improved power and capabilities have led to exponential changes that can enable leaders to combine information technology (IT) and operations technology (OT) to enable the creation and use of a digital twin. In close cooperation with MLG, NAG brings the power of robust differential equation solvers to enable real time optimisations at district and city level.

Data center energy modelling

Data Centres house the computer systems that are the UK’s digital workhouse and the backbone of the internet. The Data Centre industry is currently enjoying explosive growth due to the insatiable demand for digital services and the rapid emergence of cloud computing. Governments, NGOs, industry and environmentalists are increasingly concerned about the environmental impact and economic cost of data centre operation, which present a serious risk to the UK meetings its emissions targets.

We predominantly concentrate on the modelling of energy within these data centers. Since data centres are highly multi-disciplinary, it is vital that their energy efficiency is analysed as an integrated system. Further, Data Centres generate enormous quantities of waste heat that must be cooled in order to guarantee the reliability and operating lifetime of the electronic equipment. We have developed accurate Computational Fluid Dynamics-based models of air-cooled Data Centres and have developed new modelling approaches which enable air-cooling to be addressed in a coupled manner over the server, rack to whole data centre length-scales.

Lightweighting simulations

Vehicle lightweighting is a key R&D activity around the development of new materials and computational simulations of vehicle behaviours such as crash, NVH and durability. For example, each 100kg of mass reduction can save the environment around 8g/km of CO2. In addition to this, escalating legislation has proved to be a major driver of materials innovation in the automotive sector. Calculus Energy posses expertise in finite element and boundary element solutions applied to all aspects of lightweighting simulations.

At its core, we provide research and consultancy utilising a broad range of commercial FE/BE/Spectral codes, in addition to development of in-house mesh and meshless code, which enables new material models/code improvements to be directly implemented. Some examples of our work include the development and implementation of new elements and novel contact algorithms, development of improved or new constitutive and damage models for transient and static analysis (carbon fiber), optimisation of large structures with 1000's of design variables (black box optimization, surrogates) and the efficient implementation of models in computer codes, including as user material models in commercially available codes such as ANSYS and ABAQUS. Clients in this sector are predominantly tend to come from automotive, motorsports and aerospace OEMs. We have also been involved in research projects carrying out finite element analysis for the biomed industry.

energyplus logo ansys tm logo openfoam logo fenics logo