Multiphysics Modelling

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1. 01Enquiry and requirement assessment
2. 02Technical scoping and proposal
3. 03Execution
4. 04Quality review and delivery, with an agreed round of revisions

Read the full project workflow.

In depth: how the work is done

1. Deciding the coupling level

   We estimate characteristic time and length scales for each physics and the magnitude of cross effects. Where one field changes slowly relative to the other, a quasi-steady approach may be valid. One-way coupling transfers results, for instance temperatures from a thermal model to a structural model, without feeding back. Two-way coupling exchanges data in both directions and is needed when feedback is significant, as in strongly coupled fluid-structure interactions. Simple estimates often show that apparently complex coupling can be reduced.

2. Partitioned versus monolithic approaches

   Partitioned approaches solve each physics with its own solver and exchange data at interfaces, allowing reuse of validated solvers but risking instability for strongly coupled problems such as light structures in dense fluids. Monolithic approaches solve all fields simultaneously in one system, which is robust for strong coupling but harder to implement and more computationally demanding. Relaxation, sub-iteration and acceleration techniques can stabilise partitioned schemes. We discuss which is appropriate given tools and the strength of the coupling.

3. Scales, time stepping and interface exchange

   Physics often evolves on different time scales, which can be exploited through sub-cycling or operator splitting but must be done carefully to preserve accuracy. At interfaces, data must be mapped between meshes that may not match, conserving fluxes and energy. We check conservation across interfaces, the consistency of units and sign conventions, and the temporal alignment of exchanged quantities. These details are a frequent source of silent errors.

4. Verification, validation and sensitivity of coupled results

   Each physics should be verified separately before coupling, which isolates the source of any error. Coupled behaviour is then compared with experiments or benchmarks where possible. Because coupling adds modelling choices, we test sensitivity to the coupling scheme, the time step and the transferred quantities. Results are reported with an account of how much of the observed behaviour depends on the coupling assumptions rather than on the physics.

5. Managing computational cost and workflow

   Coupled simulations can be expensive, so planning the workflow matters. We discuss the number of cases needed, whether reduced models can be used for parameter exploration, how to restart from checkpoints and how to monitor convergence of the coupling iterations. Automation of pre-processing, exchange and post-processing reduces manual errors. The report records run times and resources so that others can judge whether similar studies are practical.

Common pitfalls this service helps avoid

• Coupling everything by default. Unneeded coupling increases cost and error sources without improving answers.
• Instability in partitioned schemes. Strongly coupled problems can diverge without relaxation or implicit treatment.
• Non-conservative data transfer. Interpolation across mismatched meshes can create or destroy energy or force.
• Validating only the final result. Without verifying single-physics parts, errors cannot be localised.

What good reporting looks like

A multiphysics report states which physics are included and why, the coupling strategy and its justification, each sub-model with its verification, interface treatment and conservation checks, the time-stepping approach, sensitivity of results to coupling choices, validation evidence and limitations. It reports computational cost so that readers can judge practicality, and it records software versions and settings to support reproduction.

An illustrative scenario

Hypothetical example written for explanation. It is not a client case, a result or a testimonial.

Imagine a study of a battery module where electrical heating raises temperatures, which in turn change electrical resistance and cause thermal expansion. A scaling estimate shows the thermal response is much slower than the electrical one, so an electro-thermal model with quasi-steady electrical behaviour is used, and the structural effect is treated one-way from temperature to stress. The researchers verify the thermal model against a known solution first, compare temperatures with measured data, and test how conclusions change if the thermal contact resistance is varied.

Questions to settle before you begin

• Which interactions are strong enough to matter for my quantity of interest?
• Can I estimate time and length scales for each physics?
• Are my individual models verified before coupling?
• How will I check conservation at interfaces?
• What data will validate the coupled behaviour?

Key terms

One-way coupling

Data pass from one physics to another without feedback.

Two-way coupling

Physics exchange data in both directions.

Partitioned scheme

Separate solvers exchange interface data.

Monolithic scheme

All fields are solved together in a single system.

Operator splitting

Solving different parts of an equation sequentially within a time step.

Working together on Computational Engineering & Modelling projects

Computational engagements begin by agreeing the question, the quantities of interest and the accuracy that matters, so that modelling effort goes where it changes the answer. We ask for geometry or system descriptions, operating conditions, material or property data and any measurements for validation. Early on, a small pilot case often checks feasibility and cost. Models are verified and, where data allow, validated before parametric results are produced. Software, versions and settings are recorded so results can be reproduced. Where inputs are missing, assumptions are listed and agreed rather than quietly filled in.

Few projects need a single service in isolation. These are the services most often combined with this one.

• Computational Engineering

  Application of numerical and computational methods to engineering problems where closed-form solutions are not available, with emphasis on model formulation, verification and validation.

• Engineering Simulation

  Simulation-based analysis of engineering components and systems, from problem definition and model set-up through post-processing and interpretation, with a clear account of what the simulation can and cannot represent.

• Heat Transfer & Thermal Simulation

  Conduction, convection and radiation analysis of components and systems, including conjugate heat transfer, transient heating and cooling, and thermal management studies.

• Finite Element Analysis (FEA)

  Finite element modelling of structures and components for stress, deformation, thermal and dynamic behaviour, with attention to meshing, element choice, boundary conditions and verification against hand calculations or tests.

• Digital Twin Modelling

  Design of model-based digital representations of physical assets that are updated from data, including the choice of fidelity, data flow and the decisions the twin is meant to support.