Publications
Journal Articles
- K. S. Kirilov et al., “Curvilinear mesh generation for the high-order virtual element method (VEM),” under review in Comput. Aided Design, April 2025. BibTeX
@unpublished{kirilov-2025b, title = {Curvilinear mesh generation for the high-order virtual element method (VEM)}, author = {Kirilov, K. S. and Zhou, J. and Peir\'o, J. and Green, M. and Moxey, D. and da Veiga, L. Beirão and Russo, A. and Dassi, F.}, journal = {under review in Comput. Aided Design}, month = apr, year = {2025}, keywords = {journal} } - M. D. Green et al., “Flight-Ready Electrical Capacitance Tomography Smartts Tank for Use with Cryogenics,” Experimental Thermal and Fluid Science, 2024, 10.1016/j.expthermflusci.2024.111144 BibTeX Abstract
@article{GREEN2023ETFS, title = {Flight-Ready Electrical Capacitance Tomography Smartts Tank for Use with Cryogenics}, journal = {Experimental Thermal and Fluid Science}, author = {Green, M. D. and Foster-Turner, R. and Hunt, A. and Ramirez-Mancebo, A. M. and Lieber, S. C. and Hartwig, J. and Moxey, D. and Tafuni, A.}, year = {2024}, doi = {10.1016/j.expthermflusci.2024.111144} }The Atout SMARTTS (SMART Tanks for Space) system allows the propellant mass distribution in a storage vessel to be measured accurately under several motion and gravity conditions and at any fill level. Based on Electrical Capacitance Tomography (ECT), SMARTTS systems incorporate electrodes on the inside of the tank, electrical connections to these electrodes, and capacitance measurements. Interpretation of the capacitance measurements is done through the Atout software, providing live images, fill levels and center of mass measurement of the propellant within the tank. The main objective of this work is to demonstrate the successful operation of a flight-ready aluminum tank with integrated SMARTTS electrodes and feedthroughs at cryogenic temperatures. The experiments presented herein consist of three submersion cycles in which the tank is lowered into an open-top dewar filled with liquid nitrogen. During the cycle, the tank is filled with liquid nitrogen when lowered into the dewar, then drained as it is lifted out. Successful operation of the SMARTTS system has been proven via live images of the fluid in the tank, as well as measured fill volume and center of mass of fluid. The materials and sensors have performed satisfactorily with no failures or post-experiment signs of damage. - M. D. Green et al., “Nekmesh: An Open-Source High-Order Mesh Generation Framework,” Computer Physics Communications, 2024, 10.1016/j.cpc.2024.109089 BibTeX Abstract
@article{GREEN2023CPC, title = {Nekmesh: An Open-Source High-Order Mesh Generation Framework}, journal = {Computer Physics Communications}, author = {Green, M. D. and Kirilov, K. S. and Turner, M. and Marcon, J. and Eichstadt, J. and Laughton, E. and Cantwell, C. D. and Sherwin, S. J. and Peiro, J. and Moxey, D.}, year = {2024}, doi = {10.1016/j.cpc.2024.109089} }High-order spectral element simulations are now becoming increasingly popular within the computational modelling community, as they offer the potential to deliver increased accuracy at reduced cost compared to traditional low-order codes. However, to support accurate, high-fidelity simulations in complex industrial applications, there is a need to generate curvilinear meshes which robustly and accurately conform to geometrical features. This is, at present, a key challenge within the mesh generation community, with only a few open-source tools able to generate curvilinear meshes for complex geometries. We present NekMesh: an open-source mesh generation package which is designed to enable the generation of valid, high-quality curvilinear meshes of complex, three-dimensional geometries for performing high-order simulations. We outline the software architecture adopted in NekMesh, which uses a pipeline of processing modules to provide a flexible, CAD-independent high-order mesh processing tool, capable of both generating meshes for a wide range of use cases, as well as post-processing linear meshes from a range of input formats for use with high-order simulations. A number of examples in various application areas are presented, with a particular emphasis on challenging aeronautical and fluid dynamics test cases. - K. Kotsarinis, M. D. Green, A. Simonini, O. Debarre, T. Magin, and A. Tafuni, “Modeling sloshing damping for spacecraft: A smoothed particle hydrodynamics application,” Aerospace Science and Technology, vol. 133, p. 108090, 2023, 10.1016/j.ast.2022.108090 BibTeX Abstract
@article{KOTSARINIS2023108090, title = {Modeling sloshing damping for spacecraft: A smoothed particle hydrodynamics application}, journal = {Aerospace Science and Technology}, volume = {133}, pages = {108090}, year = {2023}, author = {Kotsarinis, K. and Green, M. D. and Simonini, A. and Debarre, O. and Magin, T. and Tafuni, A.}, doi = {10.1016/j.ast.2022.108090} }Characterizing the movement of space propellant in the tank subjected to maneuvers and predicting its damping is a fundamental requirement for the success of space missions. In this work, we evaluate the capabilities of the smoothed particle hydrodynamics method (SPH) of characterizing liquid sloshing motion. SPH simulations are performed using the open-source code DualSPHysics, which employs a weakly compressible assumption to simulate incompressible flows. We verify the SPH scheme by showing that the calculated boundary layer matches the analytical solution of the Stokes problem. The methodology is then validated against an open-access experimental database involving sloshing experiments on partially-filled cylindrical tanks subject to horizontal excitations. We present a study of two regimes: (a) a forced, periodic regime and (b) a transient regime where we compare the full liquid interface elevation, the corresponding frequency content and the full liquid interface damping maps. The simulations are able to capture the relevant flow physics with a good level of accuracy. In particular, the simulations fairly accurately reproduced the elevation of the full free surface, predicting a 3D crescent shape of the rising wavefronts, as well as damping rates under free sloshing. Analysis of the frequency range further showed good agreement of the dominant frequencies between the experimental, simulated and analytical values given by the linearized sloshing theory. - M. D. Green, Y. Zhou, J. M. Dominguez, M. G. Gesteira, and J. Peiró, “Smooth particle hydrodynamics simulations of long-duration violent three-dimensional sloshing in tanks,” Ocean Engineering, vol. 229, p. 108925, 2021, 10.1016/j.oceaneng.2021.108925 BibTeX Abstract
@article{GREEN2021108925, title = {Smooth particle hydrodynamics simulations of long-duration violent three-dimensional sloshing in tanks}, journal = {Ocean Engineering}, volume = {229}, pages = {108925}, year = {2021}, author = {Green, Mashy D. and Zhou, Yipeng and Dominguez, José M. and Gesteira, Moncho G. and Peiró, Joaquim}, doi = {10.1016/j.oceaneng.2021.108925} }We present a smooth particle hydrodynamics (SPH) formulation that captures the sloshing frequencies of tanks and accurately simulates long-duration violent sloshing in partially filled tanks of arbitrary shape. The SPH simulations are performed using a modified version of the open-source code DualSPHysics that incorporates a density-based stabilization (δ-SPH) and imposes wall boundary conditions via ghost particles in order to achieve pressure fields without spurious spatial oscillations and to reduce non-physical energy dissipation. We verify the SPH scheme by showing that calculated sloshing wave heights, forces and natural sloshing frequencies of tanks of simple shapes, namely rectangular, cylindrical upright and spherical, match the analytical values given by the potential theory in the linear regime. The scheme is then validated by predicting the sloshing frequencies obtained experimentally in a toroidal tank and in a pill-shaped tank. Finally, we present a study of a pill-shaped tank subject to a long period of external forcing comparing simulated sloshing forces to experimental values obtained by ESA/ESTAC. The simulation is shown to fairly accurately reproduce the sloshing forces and predict the transition to swirling wave motion. Analysis of the frequency range further showed good agreement of the dominant frequencies between the experimental and simulated forces. - M. D. Green, R. Vacondio, and J. Peiró, “A smoothed particle hydrodynamics numerical scheme with a consistent diffusion term for the continuity equation,” Computers & Fluids, vol. 179, pp. 632–644, 2019, 10.1016/j.compfluid.2018.11.020 BibTeX Abstract
@article{GREEN2019632, title = {A smoothed particle hydrodynamics numerical scheme with a consistent diffusion term for the continuity equation}, journal = {Computers \& Fluids}, volume = {179}, pages = {632-644}, year = {2019}, author = {Green, Mashy D. and Vacondio, Renato and Peiró, Joaquim}, doi = {10.1016/j.compfluid.2018.11.020} }A novel formulation for the diffusive term in the continuity equation is proposed to improve the stability of smoothed particle hydrodynamics weakly compressible scheme avoiding the introduction of empirical parameters. Densities at particle-particle interface have been computed by means of a first-order consistent total variational diminishing reconstruction and a one-dimensional Roe’s approximate Riemann solver is applied to add the correct amount of diffusion. Results of numerical tests also demonstrate that the proposed method is able to guarantee consistency both inside the fluid and close to the free surface. Furthermore, a numerical analysis of several flux limiter functions has been conducted, finding that the choice of this function is a critical point to guarantee the accuracy of the method. It has been assessed, through the monitoring of the internal energy, that the van Albada limiter is more effective in dissipating spurious density fluctuations. - M. D. Green and J. Peiró, “Long duration SPH simulations of sloshing in tanks with a low fill ratio and high stretching,” Computers & Fluids, vol. 174, pp. 179–199, 2018, 10.1016/j.compfluid.2018.07.006 BibTeX Abstract
@article{GREEN2018179, title = {Long duration SPH simulations of sloshing in tanks with a low fill ratio and high stretching}, journal = {Computers \& Fluids}, volume = {174}, pages = {179-199}, year = {2018}, author = {Green, Mashy D. and Peiró, Joaquim}, doi = {10.1016/j.compfluid.2018.07.006} }Achieving stable and accurate simulations of long duration sloshing with low fill ratios using smooth particle hydrodynamics (SPH) is a challenging problem. Its solution requires a judicious choice of SPH formulation to minimize the effect of errors introduced into the simulation by boundary conditions, dissipation terms or computer arithmetic. We assess the difficulties and common pitfalls of such simulations and propose a SPH method to deal with them effectively. The formulation combines an efficient use of double precision, wall boundary conditions using ghost particles, and a δ-SPH scheme for stability with minimal energy dissipation. The proposed SPH formulation accurately matches the experimental data, both in terms of surface elevations and forces on the tank, of the study of tuned liquid dampers by Reed et al. 1998, later reproduced by ESA/ESTEC, over a wide range of frequencies. - J. Eichstädt, M. D. Green, M. Turner, J. Peiró, and D. Moxey, “Accelerating high-order mesh optimisation with an architecture-independent programming model,” Computer Physics Communications, vol. 229, pp. 36–53, 2018, 10.1016/j.cpc.2018.03.025 BibTeX Abstract
@article{EICHSTADT201836, title = {Accelerating high-order mesh optimisation with an architecture-independent programming model}, journal = {Computer Physics Communications}, volume = {229}, pages = {36-53}, year = {2018}, author = {Eichstädt, Jan and Green, Mashy D. and Turner, Michael and Peiró, Joaquim and Moxey, David}, doi = {10.1016/j.cpc.2018.03.025} }Heterogeneous manycore performance-portable programming models and libraries, such as Kokkos, have been developed to facilitate portability and maintainability of high-performance computing codes and enhance their resilience to architectural changes. Here we investigate the suitability of the Kokkos programming model for optimising the performance of the high-order mesh generator NekMesh, which has been developed to efficiently generate meshes containing millions of elements for industrial problem involving complex geometries. We describe the variational approach for a posteriori high-order mesh optimisation employed within NekMesh and its parallel implementation. We discuss its implementation for modern manycore massively parallel shared-memory CPU and GPU platforms using Kokkos and demonstrate that we achieve increased performance on multicore CPUs and accelerators compared with a native Pthreads implementation. Further, we show that we achieve additional speedup and cost reduction by running on GPUs without any hardware-specific code optimisation. - D. Moxey, M. D. Green, S. J. Sherwin, and J. Peiró, “An isoparametric approach to high-order curvilinear boundary-layer meshing,” Computer Methods in Applied Mechanics and Engineering, vol. 283, pp. 636–650, 2015, 10.1016/j.cma.2014.09.019 BibTeX Abstract
@article{MOXEY2015636, title = {An isoparametric approach to high-order curvilinear boundary-layer meshing}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {283}, pages = {636-650}, year = {2015}, author = {Moxey, D. and Green, M. D. and Sherwin, S. J. and Peiró, J.}, doi = {10.1016/j.cma.2014.09.019} }The generation of high-order curvilinear meshes for complex three-dimensional geometries is presently a challenging topic, particularly for meshes used in simulations at high Reynolds numbers where a thin boundary layer exists near walls and elements are highly stretched in the direction normal to flow. In this paper, we present a conceptually simple but very effective and modular method to address this issue. We propose an isoparametric approach, whereby a mesh containing a valid coarse discretization comprising of high-order triangular prisms near walls is refined to obtain a finer prismatic or tetrahedral boundary-layer mesh. The validity of the prismatic mesh provides a suitable mapping that allows one to obtain very fine mesh resolutions across the thickness of the boundary layer. We describe the method in detail for a high-order approximation using modal basis functions, discuss the requirements for the splitting method to produce valid prismatic and tetrahedral meshes and provide a sufficient criterion of validity in both cases. By considering two complex aeronautical configurations, we demonstrate how highly stretched meshes with sufficient resolution within the laminar sublayer can be generated to enable the simulation of flows with Reynolds numbers of 10^6 and above.
Conference Proceedings
- K. S. Kirilov, J. Peiró, J. Zhou, M. D. Green, and D. Moxey, “High-Order Curvilinear Mesh Generation From Third-Party Meshes,” in Proceedings of the 2024 International Meshing Roundtable (IMR), 2024, pp. 93–105. 10.1137/1.9781611978001.8 BibTeX Abstract
@inproceedings{KIRILOVIMR24, author = {Kirilov, Kaloyan S and Peiró, Joaquim and Zhou, Jingtian and Green, Mashy D and Moxey, David}, title = {High-Order Curvilinear Mesh Generation From Third-Party Meshes}, booktitle = {Proceedings of the 2024 International Meshing Roundtable (IMR)}, year = {2024}, pages = {93-105}, doi = {10.1137/1.9781611978001.8} }Established a posteriori mesh curving techniques often rely on an accurate CAD parametrisation of the underlying mesh objects which may not always be available. To deal with such cases, we propose a method for reconstructing the missing information between the mesh and the CAD geometry when importing an arbitrarily sourced straight-sided mesh. The reconstruction is followed by curving methods for order elevation, projections and, subsequently, optimisation. Lastly, mesh modification techniques are used to achieve the desired mesh resolution and quality. We illustrate the steps of the proposed workflow through a simple geometry and a complex automotive geometry. - K. Kirilov et al., “Curvilinear mesh generation for the high-order Virtual Element Method (VEM),” in Proceedings of the SIAM International Meshing Roundtable Workshop, 2023. BibTeX
@inproceedings{KIRILOVIMR23, author = {Kirilov, Kaloyan and Peiró, Joaquim and Green, Mashy D. and Moxey, David and da Veiga, Lourenco Beirao and Dassi, Franco and Russo, Alessandro}, title = {Curvilinear mesh generation for the high-order Virtual Element Method ({VEM})}, booktitle = {Proceedings of the SIAM International Meshing Roundtable Workshop}, year = {2023} } - M. D. Green, K. Kotsarinis, A. Simonini, O. Debarre, and A. Tafuni, “Characterization of free-surface damping in horizontally excited tanks,” in Proceedings of the 17th International SPHERIC Workshop, Rhodes, Greece, 2023. BibTeX
@inproceedings{GREEN2023SPHERIC, author = {Green, M. D. and Kotsarinis, K. and Simonini, A. and Debarre, O. and Tafuni, A.}, title = {Characterization of free-surface damping in horizontally excited tanks}, booktitle = {Proceedings of the 17th International SPHERIC Workshop, Rhodes, Greece}, year = {2023} } - E. J. Threlfall et al., “Software for Fusion Reactor Design: ExCALIBUR Project NEPTUNE:Towards Exascale Plasma Edge Simulations,” in 29th IAEA Fusion Energy Conference, GBR, Oct. 2023. Available at: https://eprints.whiterose.ac.uk/id/eprint/204359/ BibTeX Abstract
@inproceedings{wrro204359, address = {GBR}, booktitle = {29th IAEA Fusion Energy Conference}, note = {This is an author-produced version of the published paper. Uploaded in accordance with the University's Research Publications and Open Access policy.}, journal = {29th IAEA Fusion Energy Conference, proceedings}, title = {Software for Fusion Reactor Design: ExCALIBUR Project NEPTUNE:Towards Exascale Plasma Edge Simulations}, year = {2023}, month = oct, author = {Threlfall, E. J. and Akers, R. J. and Arter, W. and Barnes, M. and Barton, M. and Cantwell, C. and Challenor, P. and Cook, J. W. S. and Coveney, P. V. and Dodwell, T. and Dudson, Benjamin Daniel and Farrell, P. E. and Goffrey, T. and Green, M. and Guillas, S. and Hardman, M. and Hill, Peter Alec and Kimpton, L. and MacMackin, Chris and McMillan, B. and Moxey, D. and Mudalige, Gihan R. and Omotani, John Tomotaro and Parker, J. T. and Parra Diaz, F. and Parry, O. and Rees, T. and Ridgers, Christopher Paul and Saunders, W. and Sherwin, S. J. and Thorne, S. and Williams, J. and Wright, Steven A. and Yang, Y.}, url = {https://eprints.whiterose.ac.uk/id/eprint/204359/} }This article provides a broad overview of Project NEPTUNE, which aims to create code for simulating edge plasma physics at scales approaching the exascale, and is run by the UKAEA as part of the UK’s ExCALIBUR framework. It is a representative survey of scope and associated outputs, rather than a detailed exposition; the structure is such as to describe the core components of NEPTUNE (efforts toward simulation of plasma fluid and kinetic effects, and their synthesis into exascale-ready combined codes) and then give an indication of the wide range of other work performed under the project. - B. Liu, C. D. Cantwell, D. Moxey, M. D. Green, and S. J. Sherwin, “Vectorised spectral/hp element matrix-free operator for anisotropic heat transport in tokamak edge plasma,” in Proceedings of the 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), 2022. BibTeX
@inproceedings{LIUECCOMAS, author = {Liu, Bin and Cantwell, Chris D and Moxey, David and Green, Mashy D and Sherwin, Spencer J}, title = {Vectorised spectral/hp element matrix-free operator for anisotropic heat transport in tokamak edge plasma}, booktitle = {Proceedings of the 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS)}, year = {2022} } - M. D. Green, Y. Zhou, J. Peiró, J. M. Dominguez, and M. G. Gesteira, “Smooth particle hydrodynamics simulations of three-dimensional sloshig in tanks,” in Proceedings of the 14th International SPHERIC Workshop, Exeter, United Kingdom, 2019. BibTeX
@inproceedings{GREEN2019SPHERIC, author = {Green, M. D. and Zhou, Y. and Peiró, J. and Dominguez, J. M. and Gesteira, M. G.}, title = {Smooth particle hydrodynamics simulations of three-dimensional sloshig in tanks}, booktitle = {Proceedings of the 14th International SPHERIC Workshop, Exeter, United Kingdom}, year = {2019} } - M. D. Green, R. Vacondio, and J. Peiró, “A SPH numerical scheme with a diffusive term for the continuity equation based on Total Variational Diminishing reconstruction,” in Proceedings of the 13th International SPHERIC Workshop, Galway, Ireland, 2018. BibTeX
@inproceedings{GREEN2018SPHERIC, author = {Green, M. D. and Vacondio, R. and Peiró, J.}, title = {A SPH numerical scheme with a diffusive term for the continuity equation based on Total Variational Diminishing reconstruction}, booktitle = {Proceedings of the 13th International SPHERIC Workshop, Galway, Ireland}, year = {2018} }
Book Chapters
- D. Moxey, M. D. Green, S. J. Sherwin, and J. Peiró, “On the Generation of Curvilinear Meshes Through Subdivision of Isoparametric Elements,” in New Challenges in Grid Generation and Adaptivity for Scientific Computing, S. Perotto and L. Formaggia, Eds., Cham: Springer International Publishing, 2015, pp. 203–215. 10.1007/978-3-319-06053-8_10 BibTeX Abstract
@inbook{MOXEY2015BOOK, author = {Moxey, David and Green, Mashy D. and Sherwin, Spencer J. and Peir{\'o}, Joaquim}, editor = {Perotto, Simona and Formaggia, Luca}, title = {On the Generation of Curvilinear Meshes Through Subdivision of Isoparametric Elements}, booktitle = {New Challenges in Grid Generation and Adaptivity for Scientific Computing}, year = {2015}, publisher = {Springer International Publishing}, address = {Cham}, pages = {203--215}, isbn = {978-3-319-06053-8}, doi = {10.1007/978-3-319-06053-8_10}, url = {https://doi.org/10.1007/978-3-319-06053-8_10} }Recently, a new mesh generation technique based on the isoparametric representation of curvilinear elements has been developed in order to address the issue of generating high-order meshes with highly stretched elements. Given a valid coarse mesh comprising of a prismatic boundary layer, this technique uses the shape functions that define the geometries of the elements to produce a series of subdivided elements of arbitrary height. The purpose of this article is to investigate the range of conditions under which the resulting meshes are valid, and additionally to consider the application of this method to different element types. We consider the subdivision strategies that can be achieved with this technique and apply it to the generation of meshes suitable for boundary-layer fluid problems.
Selected Talks
- M. D. Green, I. Christidi, and M. Asif, “Custom Acceleration Frameworks: the good, the bad and the ugly,” presented at the RSE HPC SIG, 19 May, 2025.
- M. D. Green and B. Liu, “Project NEPTUNE: Towards exascale fusion simulations with Nektar++,” presented at the Nektar++ Workshop, 13-15 Sep, 2022.
- M. D. Green, “Smoothed particle hydrodynamics simulations of sloshing in three dimensional tanks,” presented at the U.K. Fluid Networks SIG Smoothed Particle Hydrodynamics, 28-29 Nov, 2019.
- M. D. Green, “Sloshing simulations with the smoothed particle hydrodynamic,” presented at the 5th Airbus/ArianeGroup Sloshing Symposium, 5-6 Nov, 2019.
- M. D. Green, “The implementation of fixed ghost particles in DualSPHysics,” presented at the Ciclo de conferencias en Ciencias de la Tierra (Lecture series in Earth Science), Universidade de Vigo, Ourense, Spain, 20th Jan, 2016.