Engineering • Mathematics • Computing • Simulation

Computational Engineering

Using mathematics, algorithms, computer science and engineering knowledge to model, simulate, analyse and optimise complex systems.

This site is maintained by Stephen Kirkup of the University of Lancashire.

What Is Computational Engineering?

Computational engineering is an interdisciplinary field that applies advanced computational methods and analysis to engineering practice. It combines engineering and physical science with applied mathematics, numerical methods, algorithms and computer programming to solve problems that are difficult to address using traditional analytical or experimental approaches.

A computational engineer develops or uses mathematical models, converts them into algorithms that computers can execute, performs simulations and analyses the resulting data. The discipline therefore sits at the intersection of engineering, mathematics and computer science. citeturn0search0turn0search4

Computational engineering is not simply “engineering with computers”. Its distinctive focus is on creating reliable mathematical and computational representations of engineering systems and using them to predict behaviour, explore alternatives and support design decisions.

Core Methods

Mathematical Modelling

Representing physical systems using equations, constitutive laws, conservation principles and other mathematical descriptions.

Numerical Analysis

Developing and analysing numerical methods for obtaining accurate approximate solutions to mathematical problems.

Algorithms

Designing computational procedures that transform mathematical models into efficient, reproducible calculations.

Optimisation

Finding improved designs, operating conditions or solutions subject to engineering constraints.

Uncertainty Quantification

Determining how uncertain inputs, parameters and model assumptions affect predictions.

Data Analysis

Extracting information from simulations, experiments and large scientific datasets to support engineering decisions.

Modelling and Simulation

Computer simulation allows engineers to investigate systems before constructing physical prototypes or conducting expensive experiments. High-fidelity simulations can represent fluid flow, heat transfer, structural deformation, electromagnetic fields, chemical processes and many other phenomena.

TechniqueTypical purpose
Finite Element Method (FEM)Structural mechanics, heat transfer, solid mechanics and multiphysics problems.
Computational Fluid Dynamics (CFD)Modelling fluid motion, turbulence, heat transfer and reacting flows.
Finite Difference MethodsNumerical solutions of differential equations on structured computational grids.
Finite Volume MethodsConservation-based numerical simulation, particularly in fluid dynamics.
Multibody DynamicsSimulation of interacting mechanical bodies and moving systems.
Monte Carlo MethodsProbabilistic simulation, uncertainty analysis and stochastic modelling.

The LinkedIn Group Computational Mechanics Research has been created to connect the people interested in the computational mechanics field. You can also link to the LinkedIn profile Numerical Analyst.

High-Performance Computing

Many computational engineering problems require far more computing power than an individual desktop can provide. High-performance computing (HPC) uses parallel processors, large memory systems, accelerators and specialised software to perform calculations at scale.

Parallel Computing

Breaking large calculations into tasks that can be processed simultaneously across many computing cores.

Scientific Software

Developing efficient, reliable and maintainable software for numerical simulation and engineering analysis.

Large-Scale Simulation

Running high-resolution models of complex physical systems that require substantial computational resources.

Visualisation

Turning large simulation datasets into graphical representations that reveal patterns, structures and physical behaviour.

Artificial Intelligence and Machine Learning

Artificial intelligence is increasingly being combined with computational engineering. Machine-learning models can accelerate simulations, construct surrogate models, identify patterns in engineering data and assist optimisation. Scientific machine learning also seeks to incorporate mathematical and physical knowledge into data-driven models.

AI does not remove the need for engineering judgement. Reliable computational engineering requires validation, verification, appropriate physical assumptions and careful assessment of uncertainty.

Applications

Aerospace Engineering

Aircraft aerodynamics, propulsion, structural dynamics, turbulence, thermal systems and spacecraft trajectories.

Mechanical Engineering

Machine design, vibration, heat transfer, fluid systems, manufacturing and product optimisation.

Civil Engineering

Structures, geotechnical systems, water resources, transport and infrastructure resilience.

Energy Engineering

Power systems, renewable energy, nuclear engineering, batteries, thermal systems and energy optimisation.

Biomedical Engineering

Blood-flow modelling, biomechanics, medical devices, imaging and computational approaches to healthcare.

Chemical Engineering

Reaction systems, process modelling, multiphase flow, transport phenomena and process optimisation.

Environmental Engineering

Climate, pollution transport, water systems, natural hazards and environmental risk.

Materials Engineering

Predicting material behaviour, microstructure, failure, processing and advanced material design.

The Computational Engineering Workflow

A typical computational engineering investigation links physical understanding, mathematical formulation, computation and validation.

StageActivity
1. Define the problemIdentify objectives, constraints, physical processes and required outputs.
2. Build the modelTranslate the engineering problem into mathematical equations and assumptions.
3. DiscretiseConvert continuous equations into a form suitable for numerical solution.
4. ImplementDevelop or configure algorithms and scientific software.
5. ComputeRun simulations using appropriate computing resources.
6. VerifyCheck that the computational implementation solves the mathematical model correctly.
7. ValidateCompare predictions with experiments, observations or trusted reference solutions.
8. AnalyseInterpret results, quantify uncertainty and use them to inform engineering decisions.

Computational Engineering and Digital Twins

A digital twin is a computational representation of a physical system that can be updated with information from the real system. Computational engineering provides many of the modelling, simulation, data-assimilation and uncertainty-quantification methods needed to develop such systems.

Digital twins can support predictive maintenance, engineering design, operational optimisation and the study of complex systems over their lifecycles.

Education and Careers

Computational engineers need a combination of engineering fundamentals, mathematics, programming and computational science. Useful skills include numerical analysis, scientific programming, simulation, data analysis, optimisation and technical communication.

Engineering R&D

Develop computational models and simulation tools for new products and technologies.

Simulation Engineering

Build, run and interpret computational models of complex engineering systems.

Scientific Computing

Develop algorithms and software for large-scale scientific and engineering computation.

Data & AI

Apply machine learning and data-driven techniques to engineering problems.

Digital Engineering

Work with digital twins, virtual prototypes and model-based engineering workflows.

Research

Progress to postgraduate research in computational engineering, applied mathematics or computational science.

Computational Engineering and Computational Science

Computational engineering is closely related to computational science and engineering (CSE). CSE lies at the intersection of mathematics and statistics, computer science, and the core disciplines of science and engineering. Computational engineering focuses particularly on using those methods for engineering analysis, design and decision-making. citeturn0search1turn0search3

Further Information

This webpage is a general educational overview of computational engineering. Specific methods, software and professional requirements vary by engineering discipline and application.