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Model reduction and multiscale methods

We develop methods that make large simulation models faster to solve and easier to use in analysis, calibration and optimisation. Through upscaling, multiscale methods and reduced models, we exploit problem structure to lower computational cost while retaining the properties that matter most for the application. Our work builds on extensive experience with flow in complex porous media and the development of simulation technology for industrial use.

What we can help you with

Detailed models can represent substantial variations in geometry and physical properties, but often become too expensive when they need to be run repeatedly. Excessive simplification, however, can remove the very relationships that govern the results. We develop methods that use information from detailed models to enable more efficient computations.

We can help you:

  • Upscale properties and flow descriptions from fine to coarser computational grids.
  • Develop multiscale methods that combine local fine-scale computations with a reduced global solve.
  • Construct fast, physics-based models for repeated simulations.
  • Adapt model resolution and complexity to the quantities of interest.
  • Use reduced models in calibration, uncertainty analysis and optimisation.
  • Assess accuracy, range of applicability and computational savings against detailed reference models.

Is your model too expensive for the studies you want to carry out? Contact our Applied Computational Science research group.

Upscaling: from fine-scale detail to effective properties

A model may contain far more detail than is practical to retain in every computation. Upscaling replaces fine-scale variations with effective properties or relationships at a coarser scale. The aim is for the coarse model to reproduce relevant aspects of the detailed model's response.

For flow in porous media, connected flow paths, barriers and permeability contrasts often play a decisive role. Simple averages are therefore not always sufficient. We work on flow-based upscaling, coarse grids and connections that account for how heterogeneity affects flow.

The properties that need to be preserved depend on the intended use. A model that reproduces pressure responses well may not capture transport and breakthrough equally well. We therefore assess upscaling against the relevant operating conditions and quantities to be predicted.

Multiscale methods: local information in global computations

Multiscale methods use local fine-scale computations to construct an efficient representation of the global problem. Local basis functions describe how variations within coarse regions influence the solution. These functions are used to assemble a smaller equation system and reconstruct a detailed approximation to the solution.

We have extensive experience developing multiscale methods for flow in heterogeneous porous media. Our work includes basis-function construction, mass-conserving flow reconstruction and adaptation to complex computational grids.

Basis functions can be reused when the problem changes moderately and updated where changes are significant. The methods can serve as approximate solvers or form part of iterative solution methods, where corrections reduce the error relative to the original discrete problem.

We also have experience bringing multiscale methods into industrial simulators. This requires them to work with wells, changing operating conditions, strong material contrasts and the simulator's overall solution strategy.

Reduced models for repeated simulations

In calibration, uncertainty analysis and optimisation, computational cost is often driven by the number of model runs. A reduced model can make these workflows feasible by representing the most important relationships with fewer degrees of freedom.

We work with coarse flow models and network models whose structure is informed by physics. Parameters and connections can be derived from a detailed model or fitted to simulation results and observations. The resulting models combine a physical computational structure with the flexibility to reproduce selected responses.

Examples include coarse-grid network models such as CGNet and simplified models of interwell connections. Read more about trainable models on our page on hybrid modelling with physics and machine learning.

Designed for the task at hand

A reduced model should be developed for a clearly defined purpose. Will it reproduce production histories, assess pressure limits, rank operating strategies or support parameter estimation? The answer determines which details must be retained, which data should be used for calibration and how model quality should be assessed.

For optimisation, the model may also need to reproduce how outputs respond to changes in control variables. Matching a single simulation trajectory is then insufficient. We can combine model reduction with differentiable simulation and sensitivity analysis to investigate and exploit these relationships.

Detailed and reduced models can also be used together: the reduced model explores many alternatives, while selected solutions are checked using the detailed simulator.

Accuracy and overall computational savings

We assess reduced models and multiscale methods against relevant reference computations. This involves examining errors in selected outputs and checking whether important properties, such as mass conservation and flow connectivity, are retained.

The total cost also includes model construction, training and updates. A method that requires substantial preparation may be highly effective for thousands of simulations but less suitable for a single run. We therefore assess computational savings across the full workflow.

Much of our experience comes from flow in porous media, where widely separated scales and strong spatial variations make efficient modelling challenging. The principles are relevant to other simulation areas, but must be adapted to the equations, structure and accuracy requirements of each application.

Selected publications