Imperial College London

DrClaireHeaney

Faculty of EngineeringDepartment of Earth Science & Engineering

Research Associate
 
 
 
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Contact

 

c.heaney Website

 
 
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Location

 

Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

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33 results found

Obeysekara A, Salinas P, Heaney CE, Kahouadji L, Via-Estrem L, Xiang J, Srinil N, Nicolle A, Matar OK, Pain CCet al., 2021, Prediction of multiphase flows with sharp interfaces using anisotropic mesh optimisation, Advances in Engineering Software, Vol: 160, Pages: 1-16, ISSN: 0965-9978

We propose an integrated, parallelised modelling approach to solve complex multiphase flow problems with sharp interfaces. This approach is based on a finite-element, double control-volume methodology, and employs highly-anisotropic mesh optimisation within a framework of high-order numerical methods and algorithms, which include adaptive time-stepping, metric advection, flux limiting, compressive advection of interfaces, multi-grid solvers and preconditioners. Each method is integral to increasing the fidelity of representing the underlying physics while maximising computational efficiency, and, only in combination, do these methods result in the accurate, reliable, and efficient simulation of complex multiphase flows and associated regime transitions. These methods are applied simultaneously for the first time in this paper, although some of the individual methods have been presented previously. We validate our numerical predictions against standard benchmark results from the literature and demonstrate capabilities of our modelling framework through the simulation of laminar and turbulent two-phase pipe flows. These complex interfacial flows involve the creation of bubbles and slugs, which involve multi-scale physics and arise due to a delicate interplay amongst inertia, viscous, gravitational, and capillary forces. We also comment on the potential use of our integrated approach to simulate large, industrial-scale multiphase pipe flow problems that feature complex topological transitions.

Journal article

Titus Z, Heaney C, Jacquemyn C, Salinas P, Jackson MD, Pain Cet al., 2021, Conditioning surface-based geological models to well data using artificial neural networks, Computational Geosciences: modeling, simulation and data analysis, Pages: 1-24, ISSN: 1420-0597

Surface-based modelling provides a computationally efficient approach for generating geometrically realistic representations of heterogeneity in reservoir models. However, conditioning Surface-Based Geological Models (SBGMs) to well data can be challenging because it is an ill-posed inverse problem with spatially distributed parameters. To aid fast and efficient conditioning, we use here SBGMs that model geometries using parametric, grid-free surfaces that require few parameters to represent even realistic geological architectures. A neural network is trained to learn the underlying process of generating SBGMs by learning the relationship between the parametrized SBGM inputs and the resulting facies identified at well locations. To condition the SBGM to these observed data, inverse modelling of the SBGM inputs is achieved by replacing the forward model with the pre-trained neural network and optimizing the network inputs using the back-propagation technique applied in training the neural network. An analysis of the uncertainties associated with the conditioned realisations demonstrates the applicability of the approach for evaluating spatial variations in geological heterogeneity away from control data in reservoir modelling. This approach for generating geologically plausible models that are calibrated with observed well data could also be extended to other geological modelling techniques such as object- and process-based modelling.

Journal article

Phillips TRF, Heaney CE, Smith PN, Pain CCet al., 2021, An autoencoder‐based reduced‐order model for eigenvalue problems with application to neutron diffusion, International Journal for Numerical Methods in Engineering, Vol: 122, Pages: 3780-3811, ISSN: 0029-5981

Using an autoencoder for dimensionality reduction, this article presents a novel projection‐based reduced‐order model for eigenvalue problems. Reduced‐order modeling relies on finding suitable basis functions which define a low‐dimensional space in which a high‐dimensional system is approximated. Proper orthogonal decomposition (POD) and singular value decomposition (SVD) are often used for this purpose and yield an optimal linear subspace. Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more efficiently, features or patterns in the high‐fidelity model results. Reduced‐order models based on an autoencoder and a novel hybrid SVD‐autoencoder are developed. These methods are compared with the standard POD‐Galerkin approach and are applied to two test cases taken from the field of nuclear reactor physics.

Journal article

Lyu Z, Lei Q, Yang L, Heaney C, Song X, Salinas P, Jackson M, Li G, Pain Cet al., 2021, A novel approach to optimising well trajectory in heterogeneous reservoirs based on the fast-marching method, Journal of Natural Gas Science and Engineering, Vol: 88, Pages: 1-12, ISSN: 1875-5100

To achieve efficient recovery of subsurface energy resources, a suitable trajectory needs to be identified for the production well. In this study, a new approach is presented for automated identification of optimum well trajectories in heterogeneous oil/gas reservoirs. The optimisation procedures are as follows. First, a productivity potential map is generated based on the site characterisation data of a reservoir (when available). Second, based on the fast-marching method, well paths are generated from a number of entrance positions to a number of exit points at opposite sides of the reservoir. The well trajectory is also locally constrained by a prescribed maximum curvature to ensure that the well trajectory is drillable. Finally, the optimum well trajectory is selected from all the candidate paths based on the calculation of a benefit-to-cost ratio. If required, a straight directional well path, may also be derived through a linear approximation to the optimised non-linear trajectory by least squares analysis. Model performance has been demonstrated in both 2D and 3D. In the 2D example, the benefit-to-cost ratio of the optimised well is much higher than that of a straight well; in the 3D example, laterals of various curvatures are generated. The applicability of the method is tested by exploring different reservoir heterogeneities and curvature constraints. This approach can be applied to determine the entrance/exit positions and the well path for subsurface energy system development, which is useful for field applications.

Journal article

Phillips T, Heaney C, Tollit B, Smith P, Pain Cet al., 2021, Reduced-order modelling with domain decomposition applied to multi-group neutron transport, Energies, Vol: 14, ISSN: 1996-1073

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

Journal article

Heaney CE, Buchan AG, Pain CC, Jewer Set al., 2021, Reduced-order modelling applied to the multigroup neutron diffusion equation using a nonlinear interpolation method for control-rod movement, Energies, ISSN: 1996-1073

Journal article

Quilodrán-Casas C, Silva VS, Arcucci R, Heaney CE, Guo Y, Pain CCet al., 2021, Digital twins based on bidirectional LSTM and GAN for modelling COVID-19

The outbreak of the coronavirus disease 2019 (COVID-19) has now spreadthroughout the globe infecting over 100 million people and causing the death ofover 2.2 million people. Thus, there is an urgent need to study the dynamics ofepidemiological models to gain a better understanding of how such diseasesspread. While epidemiological models can be computationally expensive, recentadvances in machine learning techniques have given rise to neural networks withthe ability to learn and predict complex dynamics at reduced computationalcosts. Here we introduce two digital twins of a SEIRS model applied to anidealised town. The SEIRS model has been modified to take account of spatialvariation and, where possible, the model parameters are based on official virusspreading data from the UK. We compare predictions from a data-correctedBidirectional Long Short-Term Memory network and a predictive GenerativeAdversarial Network. The predictions given by these two frameworks are accuratewhen compared to the original SEIRS model data. Additionally, these frameworksare data-agnostic and could be applied to towns, idealised or real, in the UKor in other countries. Also, more compartments could be included in the SEIRSmodel, in order to study more realistic epidemiological behaviour.

Journal article

Heaney CE, Li Y, Matar OK, Pain CCet al., 2020, Applying Convolutional Neural Networks to Data on Unstructured Meshes with Space-Filling Curves, arxiv

This paper presents the first classical Convolutional Neural Network (CNN)that can be applied directly to data from unstructured finite element meshes orcontrol volume grids. CNNs have been hugely influential in the areas of imageclassification and image compression, both of which typically deal with data onstructured grids. Unstructured meshes are frequently used to solve partialdifferential equations and are particularly suitable for problems that requirethe mesh to conform to complex geometries or for problems that require variablemesh resolution. Central to the approach are space-filling curves, whichtraverse the nodes or cells of a mesh tracing out a path that is as short aspossible (in terms of numbers of edges) and that visits each node or cellexactly once. The space-filling curves (SFCs) are used to find an ordering ofthe nodes or cells that can transform multi-dimensional solutions onunstructured meshes into a one-dimensional (1D) representation, to which 1Dconvolutional layers can then be applied. Although developed in two dimensions,the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutionalautoencoder (CAE) although other types of CNN could be used. The approach istested by applying CAEs to data sets that have been reordered with an SFC.Sparse layers are used at the input and output of the autoencoder, and the useof multiple SFCs is explored. We compare the accuracy of the SFC-based CAE withthat of a classical CAE applied to two idealised problems on structured meshes,and then apply the approach to solutions of flow past a cylinder obtained usingthe finite-element method and an unstructured mesh.

Journal article

Titus Z, Pain C, Jacquemyn C, Salinas P, Heaney C, Jackson Met al., 2020, Conditioning surface-based geological models to well data using neural networks

Generating representative reservoir models that accurately describe the spatial distribution of geological heterogeneities is crucial for reliable predictions of historic and future reservoir performance. Surface-based geological models (SBGMs) have been shown to better capture complex reservoir architecture than grid-based methods; however, conditioning such models to well data can be challenging because it is an ill-posed inverse problem with spatially distributed parameters. Here, we propose the use of deep Convolutional Neural Networks (CNNs) to generate geologically plausible SBGMs that honour well data. Deep CNNs have previously demonstrated capability in learning representative features of spatially correlated data for large scale and highly non-linear geophysical systems similar to those encountered in subsurface reservoirs. In the work reported here, a CNN is trained to learn the relationship between parameterised inputs to SBGM, the resulting geometry and heterogeneity distribution, and the mis-match between model surfaces and well data. We show that the trained CNN can generate a range of geologically plausible models that honour well data. The method is demonstrated for a 2D example model, representing a shallow marine reservoir and a 3D extension of the model that captures typical heterogeneities encountered in the subsurface such as parasequences, clinoforms and facies boundaries. These test cases highlight the improvement in reservoir characterisation for realistic geological cases. We present here a method of generating geologically consistent reservoir models that match well data. The developed method will allow the generation of new high-fidelity realizations of subsurface geology conditioned to information at wells, which is the most direct observational data that can be acquired. Technical Contributions - The use of surface-based modelling to describe even complex geological features compared to grid-based modelling significantly decreases the co

Conference paper

Salinas P, Jacquemyn C, Heaney C, Pain C, Jackson Met al., 2020, Well location optimisation by using surface-based modelling and dynamic mesh optimisation

Predictions of production obtained by numerical simulation often depend on grid resolution as fine resolution is required to resolve key aspects of flow. Moreover, the controls on flow can depend on well location in a model. In some cases, it may be key to capture coning or cusping; in others, it might be the location of specific high permeability thief zones or low permeability flow barriers. Thus, models with a suitable grid resolution for one particular set of well locations may fail to properly capture key aspects of flow if the wells are moved. During well optimisation, it is impossible to predict a-priori which well locations will be tested in a given model. Thus, it is unlikely to know a-priori if the grid resolution is suitable for all possible locations tested during a well optimisation procedure on a single model, and the problem is even more profound if well optimisation is tested over a range of different models. Here, we report an optimisation methodology based on Dynamic Mesh Optimisation (DMO). DMO will produce optimised meshes for a given model, set of well locations, pressure (and other key fields) distribution and timelevel. Grid-free Surface-Based Modelling (SBM) models are automatically generated in which well trajectories are introduced (also not constrained by a mesh), respected by DMO. For the optimization of the well location a Genetic Algorithm (GA) approach is used, more specifically the open-source software package DEAP. DMO ensures that all the models automatically generated and simulated in the optimisation process are modelled with an equivalent mesh resolution without user interaction, in this way, the local pressure drawdown and associated physical effects (such as coning or cusping) can be properly captured if they appear in any of the many scenarios that are studied . We demonstrate that the method has wide application in reservoir-scale models of oil and gas fields, and regional models of groundwater resources.

Conference paper

Xiao D, Fang F, Heaney CE, Navon IM, Pain CCet al., 2019, A domain decomposition method for the non-intrusive reduced order modelling of fluid flow, Computer Methods in Applied Mechanics and Engineering, Vol: 354, Pages: 307-330, ISSN: 0045-7825

In this paper we present a new domain decomposition non-intrusive reduced order model (DDNIROM) for the Navier–Stokes equations. The computational domain is partitioned into subdomains and a set of local basis functions is constructed in each subdomain using Proper Orthogonal Decomposition (POD). A radial basis function (RBF) method is then used to generate a set of hypersurfaces for each subdomain. Each local hypersurface represents, not only the fluid dynamics over the subdomain to which it belongs, but also the interactions with the surrounding subdomains. This implicit coupling between the subdomains provides the global coupling necessary to enforce incompressibility and is a means of providing boundary conditions for each subdomain.The performance of this DDNIROM is illustrated numerically by three examples: flow past a cylinder, and air flow over 2D and 3D street canyons. The results show that the DDNIROM exhibits good agreement with the high-fidelity full model while the computational cost is reduced by several orders of magnitude. The domain decomposition (DD) method provides the flexibility to choose different numbers of local basis functions for each subdomain depending on the complexity of the flow therein. The fact that the RBF surface representation takes input only from its current subdomain and the surrounding subdomains, means that, crucially, there is a reduction in the dimensionality of the hypersurface when compared with a more traditional, global NIROM. This comes at the cost of having a larger number of hypersurfaces.

Journal article

Xiao D, Heaney CE, Fang F, Mottet L, Hu R, Bistrian DA, Aristodemou E, Navon IM, Pain CCet al., 2019, A domain decomposition non-intrusive reduced order model for turbulent flows, Computers and Fluids, Vol: 182, Pages: 15-27, ISSN: 0045-7930

In this paper, a new Domain Decomposition Non-Intrusive Reduced Order Model (DDNIROM) is developed for turbulent flows. The method works by partitioning the computational domain into a number of subdomains in such a way that the summation of weights associated with the finite element nodes within each subdomain is approximately equal, and the communication between subdomains is minimised. With suitably chosen weights, it is expected that there will be approximately equal accuracy associated with each subdomain. This accuracy is maximised by allowing the partitioning to occur through areas of the domain that have relatively little flow activity, which, in this case, is characterised by the pointwise maximum Reynolds stresses.A Gaussian Process Regression (GPR) machine learning method is used to construct a set of local approximation functions (hypersurfaces) for each subdomain. Each local hypersurface represents not only the fluid dynamics over the subdomain it belongs to, but also the interactions of the flow dynamics with the surrounding subdomains. Thus, in this way, the surrounding subdomains may be viewed as providing boundary conditions for the current subdomain.We consider a specific example of turbulent air flow within an urban neighbourhood at a test site in London and demonstrate the effectiveness of the proposed DDNIROM.

Journal article

Xiao D, Heaney CE, Mottet L, Fang F, Lin W, Navon IM, Guo Y, Matar OK, Robins AG, Pain CCet al., 2019, A reduced order model for turbulent flows in the urban environment using machine learning, Building and Environment, Vol: 148, Pages: 323-337, ISSN: 0360-1323

To help create a comfortable and healthy indoor and outdoor environment in which to live, there is a need to understand turbulent air flows within the urban environment. To this end, building on a previously reported method [1], we develop a fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows found within an urban environment. To resolve larger scale turbulent fluctuations, we employ a Large Eddy Simulation (LES) model and solve the resulting computational model on unstructured meshes. The objective is to construct a rapid-running NIROM from these results that will have ‘similar’ dynamics to the original LES model. Based on Proper Orthogonal Decomposition (POD) and machine learning techniques, this Reduced Order Model (ROM) is six orders of magnitude faster than the high-fidelity LES model and we demonstrate how ‘similar’ it can be to the high-fidelity model by comparing statistical quantities such as the mean flows, Reynolds stresses and probability densities of the velocities. We also include validation of the high-fidelity model against data from wind tunnel experiments.This paper represents a key step towards the use of reduced order modelling for operational purposes with the tantalising possibility of it being used in place of Gaussian plume models, and the potential for greatly improved model fidelity and confidence.

Journal article

Salinas P, Jacquemyn C, Kampitsis A, Via-Estrem L, Heaney C, Pain C, Jackson Met al., 2019, A parallel load-balancing reservoir simulator with dynamic mesh optimisation

Copyright 2019, Society of Petroleum Engineers. The use of dynamic mesh optimization (DMO) for multiphase flow in porous have been proposed recently showing a very good potential to reduce the computational cost by placing the resolution where and when necessary. Nonetheless, further work needs to be done to prove its usability in very large domains where parallel computing with distributed memory, i.e. using MPI libraries, may be necessary. Here, we describe the methodology used to parallelize a multiphase porous media flow simulator in combination with DMO as well as study of its performance. Due to the peculiarities and complexities of the typical porous media simulations due to its high aspect ratios, we have included a fail-safe for parallel simulations with DMO that enhance the robustness and stability of the methods used to parallelize DMO in other fields (Navier-Stokes flows). The results show that DMO for parallel computing in multiphase porous media flows can perform very well, showing good scaling behaviour.

Conference paper

Salinas P, Jacquemyn C, Kampitsis A, Via-Estrem L, Heaney C, Pain C, Jackson Met al., 2019, A parallel load-balancing reservoir simulator with dynamic mesh optimisation

Copyright 2019, Society of Petroleum Engineers. The use of dynamic mesh optimization (DMO) for multiphase flow in porous have been proposed recently showing a very good potential to reduce the computational cost by placing the resolution where and when necessary. Nonetheless, further work needs to be done to prove its usability in very large domains where parallel computing with distributed memory, i.e. using MPI libraries, may be necessary. Here, we describe the methodology used to parallelize a multiphase porous media flow simulator in combination with DMO as well as study of its performance. Due to the peculiarities and complexities of the typical porous media simulations due to its high aspect ratios, we have included a fail-safe for parallel simulations with DMO that enhance the robustness and stability of the methods used to parallelize DMO in other fields (Navier-Stokes flows). The results show that DMO for parallel computing in multiphase porous media flows can perform very well, showing good scaling behaviour.

Conference paper

Salinas P, Jacquemyn C, Kampitsis A, Via-Estrem L, Heaney C, Pain C, Jackson Met al., 2019, A parallel load-balancing reservoir simulator with dynamic mesh optimisation

Copyright 2019, Society of Petroleum Engineers. The use of dynamic mesh optimization (DMO) for multiphase flow in porous have been proposed recently showing a very good potential to reduce the computational cost by placing the resolution where and when necessary. Nonetheless, further work needs to be done to prove its usability in very large domains where parallel computing with distributed memory, i.e. using MPI libraries, may be necessary. Here, we describe the methodology used to parallelize a multiphase porous media flow simulator in combination with DMO as well as study of its performance. Due to the peculiarities and complexities of the typical porous media simulations due to its high aspect ratios, we have included a fail-safe for parallel simulations with DMO that enhance the robustness and stability of the methods used to parallelize DMO in other fields (Navier-Stokes flows). The results show that DMO for parallel computing in multiphase porous media flows can perform very well, showing good scaling behaviour.

Conference paper

Salinas P, Jacquemyn C, Kampitsis A, Via-Estrem L, Heaney C, Pain C, Jackson Met al., 2019, A parallel load-balancing reservoir simulator with dynamic mesh optimisation

The use of dynamic mesh optimization (DMO) for multiphase flow in porous have been proposed recently showing a very good potential to reduce the computational cost by placing the resolution where and when necessary. Nonetheless, further work needs to be done to prove its usability in very large domains where parallel computing with distributed memory, i.e. using MPI libraries, may be necessary. Here, we describe the methodology used to parallelize a multiphase porous media flow simulator in combination with DMO as well as study of its performance. Due to the peculiarities and complexities of the typical porous media simulations due to its high aspect ratios, we have included a fail-safe for parallel simulations with DMO that enhance the robustness and stability of the methods used to parallelize DMO in other fields (Navier-Stokes flows). The results show that DMO for parallel computing in multiphase porous media flows can perform very well, showing good scaling behaviour.

Conference paper

Heaney C, Salinas P, Pain C, Fang F, Navon Met al., 2018, Well Optimisation With Goal-Based Sensitivity Maps Using Time Windows And Ensemble Perturbations, European conference on mathematics of oil recovery

Conference paper

Salinas-Cortes P, Pain CC, Osman H, Heaney C, Pavlidis D, Jackson MDet al., 2018, Vanishing artificial capillary pressure for improved real-size reservoir simulations

A common approach to stabilise the system arising from the discretisation of the advection equation is to introduce artificial diffusion. However, introducing artificial diffusion affects the result, therefore a balance has to be found so that the introduced artificial diffusion does not affects the final result. Recently, a vanishing artificial diffusion was presented. In that method, the diffusion was controlled by the convergence of the non-linear solver by multiplying the artificial diffusion term by the difference between the most recent saturation estimation and the one obtained in the previous non-linear iteration. This approach showed that it is capable to help to reduce the computational effort required by the non-linear solver, as classical artificial diffusions do. However, this approach could lead to an introduction of an artificial source/sink in the system, therefore not conserving mass. A conservative vanishing artificial diffusion is presented here. It improves the convergence and convergence rate of the non-linear solver by reducing the non-linearity of the equations. Moreover, it is tailored to specially help to deal with the capillary pressure. The vanishing artificial diffusion is introduced using the same model employed to introduce the capillary pressure, obtaining a vanishing artificial capillary pressure diffusion term. By solving this term implicitly in the saturation equation, a very efficient method to model multiphase porous media flow with physical capillary pressure is obtained. This is tested in real-size reservoir simulations with realistically high capillary numbers to prove its efficiency. The presented method provides accurate results and significantly reduces the effort required by the non-linear solver to achieve convergence. It enables to carry out very demanding numerical simulations, e.g. when the physical capillary pressure effects are dominant, with Courant numbers that are at least two orders of magnitude bigger than withou

Conference paper

Heaney CE, Salinas P, Pain CC, Fang F, Navon IMet al., 2018, Well optimisation with goal-based sensitivity maps using time windows and ensemble perturbations

Knowledge of the sensitivity of a solution to small changes in the model parameters is exploited in many areas in computational physics and used to perform mesh adaptivity, or to correct errors based on discretisation and sub-grid-scale modelling errors, to perform the assimilation of data based on adjusting the most sensitive parameters to the model-observation misfit, and similarly to form optimised sub-grid-scale models. We present a goal-based approach for forming sensitivity (or importance) maps using ensembles. These maps are defined as regions in space and time of high relevance for a given goal, for example, the solution at an observation point within the domain. The presented approach relies solely on ensembles obtained from the forward model and thus can be used with complex models for which calculating an adjoint is not a practical option. This provides a simple approach for optimisation of sensor placement, goal based mesh adaptivity, assessment of goals and data assimilation. We investigate methods which reduce the number of ensembles used to construct the maps yet which retain reasonable fidelity of the maps. The fidelity comes from an integrated method including a goal-based approach, in which the most up-to-date importance maps are fed back into the perturbations to focus the algorithm on the key variables and domain areas. Also within the method smoothing is applied to the perturbations to obtain a multi-scale, global picture of the sensitivities; the perturbations are orthogonalised in order to generate a well-posed system which can be inverted; and time windows are applied (for time dependent problems) where we work backwards in time to obtain greater accuracy of the sensitivity maps. The approach is demonstrated on a multi-phase flow problem.

Conference paper

Salinas P, Jacquemyn C, Heaney C, Pavlidis D, Pain C, Jackson Met al., 2018, Simulation of enhanced geothermal systems using dynamic unstructured mesh optimisation

© 2018 Society of Petroleum Engineers. All rights reserved. Recently, a novel method for heat extraction from geothermal reservoirs has been proposed, it is named radiator enhance geothermal system (RAD-EGS). In this method, the heat is extracted by placing two horizontal wells separated vertically, and injecting the cold water in the deepest one. Modelling a geothermal reservoir with wells can be very challenging as the scales to be considered can span several orders of magnitude. Around the wells (metres scale) it is well known that there is a high-pressure drawdown, while the dimensions of the reservoir are typically of many kilometres. Modelling across these scales using a fixed mesh can be computationally very expensive. Here, an unstructured dynamic mesh optimisation method is used to dynamically optimise the mesh to the fields of interest such as temperature and/or pressure to ensure that a certain precision across the domain is obtained. This methodology places the resolution where and when necessary, reducing the number of elements to ensure a certain accuracy when compared to an equivalent fixed mesh. Wells are represented using a 1D line which is represented by a line vector, whose position is not modified when adapting the mesh.

Conference paper

Heaney CE, Pain CC, Buchan AG, Jewer Set al., 2018, Reactor simulators and reduced order modeling, Nuclear Future, Vol: 14, Pages: 49-54, ISSN: 1745-2058

The high quality real-time solutions offered by Reduced Order Modelling (ROM) could greatly improve the resolution of the solution available in training simulators and would add significantly to a student's understanding. ROM will be a key component of the modelling of reactor simulators, the operational modelling of reactors and accident analysis. The computational speed of this unique framework will enable real-time interactive use, uncertainty analysis, rapid data assimilation and better-informed reactor management. The goal of a real-time response has been realised in the reduced-order model of a fuel assembly presented here.

Journal article

Thanh HO, Heaney CE, Lee C-K, Liu GR, Nguyen-Xuan Het al., 2015, On stability, convergence and accuracy of bES-FEM and bFS-FEM for nearly incompressible elasticity, COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, Vol: 285, Pages: 315-345, ISSN: 0045-7825

Journal article

Heaney CE, Bonnier PG, Brinkgreve RBJ, Hicks MAet al., 2013, An adaptive mesh refinement algorithm based on element subdivision with application to geomaterials, Pages: 315-324

The implementation of Adaptive Mesh Refinement (AMR) within the geotech- nical software package PLAXIS 2D is described in this paper. A recovery-based algorithm is used which aims to reduce the discretisation error by refining the mesh during the solution process. The error is estimated with a Zienkiewicz-Zhu-type error estimator but based on the incremental deviatoric strain instead of stress. The deviatoric strain field is compared with an improved field calculated by superconvergent patch recovery. Once elements with large errors have been detected, mesh refinement takes place. A combination of regular subdivision and longest-edge bisection is employed. Mapping history variables from the old mesh to the new mesh is accomplished by using the recovered solutions and the shape functions. The AMR algorithm is demonstrated for a biaxial compression test.

Conference paper

Coombs WM, Crouch RS, Heaney CE, 2013, Observations on Mohr-Coulomb Plasticity under Plane Strain, JOURNAL OF ENGINEERING MECHANICS, Vol: 139, Pages: 1218-1228, ISSN: 0733-9399

Journal article

Heaney CE, Brinkgreve RBJ, Bonnier PG, Hicks MAet al., 2013, Adaptive Mesh Refinement for strain-softening materials in geomechanics, International Conference on Installation Effects in Geotechnical Engineering (ICIEGE), Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 8-14

Conference paper

Zhuang X, Heaney C, Augarde C, 2012, On error control in the element-free Galerkin method, ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, Vol: 36, Pages: 351-360, ISSN: 0955-7997

Journal article

Heaney CE, Augarde CE, Deeks AJ, Coombs WM, Crouch RSet al., 2010, Advances in meshless methods with application to geotechnics, Pages: 239-244

Finite element methods are well-established for modelling problems in geotechnics involving elasto-plastic constitutive models. However, meshless methods could offer some advantages for problems involving finite deformations as the mesh entanglement problem is then removed. In addition, major savings could be made in the pre-processing stage for 3D problems. Both of these features are of interest to geotechnical modellers. In this paper we review the use of meshless methods for modelling plasticity, highlighting some potential problems particular to the methods' formulations. We then demonstrate the use of a recently developed hybrid method based on the meshless local Petrov-Galerkin method for some simple examples in elasto-plasticity and show that there are important issues to be considered. Finally we comment briefly on the amendments required for modelling finite deformation, which are underway. © 2010 Taylor & Francis Group, London.

Conference paper

Heaney C, Augarde C, Deeks A, 2010, Modelling Elasto-Plasticity Using the Hybrid MLPG Method, CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, Vol: 56, Pages: 153-177, ISSN: 1526-1492

Journal article

Augarde C, Heaney C, 2009, The use of meshless methods in geotechnics, Pages: 311-320

Numerical modelling in industrial and (to a lesser extent) academic geotechnics for continuum problems is dominated by the finite element method (FEM). The reasons for this are the robustness of current commercial codes and their ease of use. As engineers become ever more ambitious and wish to analyze larger systems, however, the difficulties associated with finite element methods become of greater significance. Issues such as mesh generation and regeneration for adaptivity become considerably more difficult in moving to very large 3D models, and when one wishes also to include finite deformation, for instance. Meshless (or meshfree) methods offer a solution to these difficulties with the FEM as they do not require a mesh. These techniques are considerably younger than finite element methods and have yet to be properly commercialized. Many issues remain to be resolved before they will compete with the FEM, such as how essential boundary conditions are dealt with. In this paper we outline some current uses of meshless methods in geotechnics and highlight work which combines a meshless method with another novel numerical method for problems in geotechnics.

Conference paper

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