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    Collins GS, Lynch E, McAdam R, Davison TMet al., 2017,

    A numerical assessment of simple airblast models of impact airbursts

    , METEORITICS & PLANETARY SCIENCE, Vol: 52, Pages: 1542-1560, ISSN: 1086-9379
    Watters WA, Hundal CB, Radford A, Collins GS, Tornabene LLet al., 2017,

    Dependence of secondary crater characteristics on downrange distance: High-resolution morphometry and simulations

    , JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS, Vol: 122, Pages: 1773-1800, ISSN: 2169-9097
    Davison TM, Derrick JG, Collins GS, Bland PA, Rutherford ME, Chapman DJ, Eakins DEet al., 2017,

    Impact-induced compaction of primitive solar system solids: The need for mesoscale modelling and experiments

    , 14TH HYPERVELOCITY IMPACT SYMPOSIUM (HVIS 2017), Vol: 204, Pages: 405-412, ISSN: 1877-7058
    Morgan JV, Gulick SPS, Bralower T, Chenot E, Christeson G, Claeys P, Cockell CS, Collins GS, Coolen MJL, Ferriere L, Gebhardt C, Goto K, Jones H, Kring DA, Le Ber E, Lofi J, Long X, Lowery C, Mellett C, Ocampo-Torres R, Osinski GR, Perez-Cruz L, Pickersgill A, Poelchau M, Rae A, Rasmussen C, Rebolledo-Vieyra M, Riller U, Sato H, Schmitt DR, Smit J, Tikoo S, Tomioka N, Urrutia-Fucugauchi J, Whalen M, Wittmann A, Yamaguchi KE, Zylberman Wet al., 2016,

    The formation of peak rings in large impact craters

    , SCIENCE, Vol: 354, Pages: 878-882, ISSN: 0036-8075
    Johnson BC, Blair DM, Collins GS, Melosh HJ, Freed AM, Taylor GJ, Head JW, Wieczorek MA, Andrews-Hanna JC, Nimmo F, Keane JT, Miljkovic K, Soderblom JM, Zuber MTet al., 2016,

    Formation of the Orientale lunar multiring basin

    , SCIENCE, Vol: 354, Pages: 441-444, ISSN: 0036-8075
    Kring DA, Kramer GY, Collins GS, Potter RWK, Chandnani Met al., 2016,

    Peak-ring structure and kinematics from a multi-disciplinary study of the Schrodinger impact basin

    , NATURE COMMUNICATIONS, Vol: 7, ISSN: 2041-1723
    Bhutani G, Brito-Parada PR, Cilliers JJ, 2016,

    Polydispersed flow modelling using population balances in an adaptive mesh finite element framework

    , COMPUTERS & CHEMICAL ENGINEERING, Vol: 87, Pages: 208-225, ISSN: 0098-1354
    Jacobs CT, Avdis A, Mouradian SL, Piggott MDet al., 2015,

    Integrating Research Data Management into Geographical Information Systems

    ,, 5th International Workshop on Semantic Digital Archives (SDA 2015), Pages: 7-17

    Ocean modelling requires the production of high-fidelity computational meshes upon which to solve the equations of motion. The production of such meshes by hand is often infeasible, considering the complexity of the bathymetry and coastlines. The use of Geographical Information Systems (GIS) is therefore a key component to discretising the region of interest and producing a mesh appropriate to resolve the dynamics. However, all data associated with the production of a mesh must be provided in order to contribute to the overall recomputability of the subsequent simulation. This work presents the integration of research data management in QMesh, a tool for generating meshes using GIS. The tool uses the PyRDM library to provide a quick and easy way for scientists to publish meshes, and all data required to regenerate them, to persistent online repositories. These repositories are assigned unique identifiers to enable proper citation of the meshes in journal articles.

    Anderson RM, 2015,


    , Publisher: ROYAL SOC
    Jackson MD, Percival JR, Mostaghiml P, Tollit BS, Pavlidis D, Pain CC, Gomes JLMA, El-Sheikh AH, Salinas P, Muggeridge AH, Blunt MJet al., 2015,

    Reservoir Modeling for Flow Simulation by Use of Surfaces, Adaptive Unstructured Meshes, and an Overlapping-Control-Volume Finite-Element Method

    , SPE RESERVOIR EVALUATION & ENGINEERING, Vol: 18, Pages: 115-132, ISSN: 1094-6470
    Guo X, Lange M, Gorman G, Mitchell L, Weiland Met al., 2015,

    Developing a scalable hybrid MPI/OpenMP unstructured finite element model

    , COMPUTERS & FLUIDS, Vol: 110, Pages: 227-234, ISSN: 0045-7930
    Potter RWK, Kring DA, Collins GS, 2015,

    Scaling of basin-sized impacts and the influence of target temperature

    , Special Paper of the Geological Society of America, Vol: 518, Pages: 99-113, ISSN: 0072-1077

    © 2015 The Geological Society of America. All rights reserved. We produce a set of scaling laws for basin-sized impacts using data from a suite of lunar basin numerical models. The results demonstrate the importance of preimpact target temperature and thermal gradient, which are shown to greatly influence the modification phase of the impact cratering process. Impacts into targets with contrasting thermal properties also produce very different crustal and topographic profiles for impacts of the same energy. Thermal conditions do not, however, significantly influence the excavation stage of the cratering process; results demonstrate, as a consequence of gravity-dominated growth, that transient crater radii are generally within 5% of each other over a wide range of thermal gradients. Excavation depth-to-diameter ratios for the basin models (~0.12) agree well with experimental, geological, and geophysical estimates, suggesting basins follow proportional scaling. This is further demonstrated by an agreement between the basin models and Piscaling laws based upon first principles and experimental data. The results of this work should also be applicable to basin-scale impacts on other silicate bodies, including the Hadean Earth.

    Salinas P, Percival JR, Pavlidis D, Xie Z, Gomes J, Pain CC, Jackson MDet al., 2015,

    A discontinuous overlapping control volume finite element method for multi-phase porous media flow using dynamic unstructured mesh optimization

    , Pages: 1511-1528

    Copyright © 2015, Society of Petroleum Engineers. We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous Nth- order representation for pressure and (N+1)th-order for velocity. The method conserves mass and ensures that the extended Darcy equations for multi-phase flow are exactly enforced, but does not require the use of control volumes (CVs) that span domain boundaries. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic features such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, in conjunction with dynamic mesh optimization, in which the mesh adapts in space and time to key solution fields such as pressure, velocity or saturation whilst honoring a surface-based representation of the underlying geologic heterogeneity, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The work presented is significant for two reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media; second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization without compromising parallelization.

    Pavlidis D, Gomes JLMA, Salinas P, Pain CC, Tehrani AAK, Moatamedi M, Smith PN, Jones AV, Matar OKet al., 2015,

    Numerical modelling of debris bed water quenching

    Miljkovic K, Wieczorek MA, Collins GS, Solomon SC, Smith DE, Zuber MTet al., 2015,

    Excavation of the lunar mantle by basin-forming impact events on the Moon

    , EARTH AND PLANETARY SCIENCE LETTERS, Vol: 409, Pages: 243-251, ISSN: 0012-821X
    Jacobs CT, Goldin TJ, Collins GS, Piggott MD, Kramer SC, Melosh HJ, Wilson CRG, Allison PAet al., 2015,

    An improved quantitative measure of the tendency for volcanic ash plumes to form in water: implications for the deposition of marine ash beds

    , JOURNAL OF VOLCANOLOGY AND GEOTHERMAL RESEARCH, Vol: 290, Pages: 114-124, ISSN: 0377-0273
    Jacobs CT, Piggott MD, 2015,

    Firedrake-Fluids v0.1: numerical modelling of shallow water flows using an automated solution framework

    , GEOSCIENTIFIC MODEL DEVELOPMENT, Vol: 8, Pages: 533-547, ISSN: 1991-959X
    Bland PA, Collins GS, Davison TM, Abreu NM, Ciesla FJ, Muxworthy AR, Moore Jet al., 2014,

    Pressure-temperature evolution of primordial solar system solids during impact-induced compaction

    , NATURE COMMUNICATIONS, Vol: 5, ISSN: 2041-1723
    Collins GS, 2014,

    Numerical simulations of impact crater formation with dilatancy

    , JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS, Vol: 119, Pages: 2600-2619, ISSN: 2169-9097
    Hill J, Collins GS, Avdis A, Kramer SC, Piggott MDet al., 2014,

    How does multiscale modelling and inclusion of realistic palaeobathymetry affect numerical simulation of the Storegga Slide tsunami?

    , Ocean Modelling, Vol: 83, Pages: 11-25, ISSN: 1463-5003

    The ∼8.15 ka Storegga submarine slide was a large (∼3000 km3), tsunamigenic slide off the coast of Norway. The resulting tsunami had run-up heights of around 10–20 m on the Norwegian coast, over 12 m in Shetland, 3–6 m on the Scottish mainland coast and reached as far as Greenland. Accurate numerical simulations of Storegga require high spatial resolution near the coasts, particularly near tsunami run-up observations, and also in the slide region. However, as the computational domain must span the whole of the Norwegian-Greenland sea, employing uniformly high spatial resolution is computationally prohibitive. To overcome this problem, we present a multiscale numerical model of the Storegga slide-generated tsunami where spatial resolution varies from 500 m to 50 km across the entire Norwegian-Greenland sea domain to optimally resolve the slide region, important coastlines and bathymetric changes. We compare results from our multiscale model to previous results using constant-resolution models and show that accounting for changes in bathymetry since 8.15 ka, neglected in previous numerical studies of the Storegga slide-tsunami, improves the agreement between the model and inferred run-up heights in specific locations, especially in the Shetlands, where maximum run-up height increased from 8 m (modern bathymetry) to 13 m (palaeobathymetry). By tracking the Storegga tsunami as far south as the southern North sea, we also found that wave heights were high enough to inundate Doggerland, an island in the southern North Sea prior to sea level rise over the last 8 ka.

    Jacobs CT, Avdis A, Gorman GJ, Piggott MDet al., 2014,

    PyRDM: A Python-based Library for Automating the Management and Online Publication of Scientific Software and Data

    , Journal of Open Research Software, Vol: 2, ISSN: 2049-9647
    Jacobs CT, Piggott MD, 2014,


    Mostaghimi P, Tollit BS, Neethling SJ, Gorman GJ, Pain CCet al., 2014,

    A control volume finite element method for adaptive mesh simulation of flow in heap leaching

    , JOURNAL OF ENGINEERING MATHEMATICS, Vol: 87, Pages: 111-121, ISSN: 0022-0833
    Jacobs CT, Avdis A, Gorman GJ, Piggott MDet al., 2014,


    PyRDM is a Python-based library for research data management (RDM). It facilitates the automated publication of scientific software and associated input and output data.

    Funke SW, Farrell PE, Piggott MD, 2014,

    Tidal turbine array optimisation using the adjoint approach

    , RENEWABLE ENERGY, Vol: 63, Pages: 658-673, ISSN: 0960-1481
    Xie Z, 2014,

    Numerical modelling of wind effects on breaking solitary waves

    , European Journal of Mechanics, B/Fluids, Vol: 43, Pages: 135-147, ISSN: 0997-7546

    Wind effects on breaking solitary waves are investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier-Stokes equations with the k - . turbulence model simultaneously for the flows both in the air and water, with the air-water interface calculated by the volume of fluid method. First, the proposed model was validated with the computations of a breaking solitary wave run-up on a 1:19.85 sloping beach in the absence of wind, and fairly good agreement between the computational results and experimental measurements was obtained. Further, detailed information of the water surface profiles, velocity fields, vorticity, turbulent stress, maximum run-up, evolution of maximum wave height, energy dissipation, plunging jet and splash-up phenomena is presented and discussed for breaking solitary waves in the presence of wind. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity and turbulent stress, and affects the solitary wave shoaling, breaking and run-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment. © 2013 Elsevier Masson SAS. All rights reserved.

    Buchan AG, Farrell PE, Gorman GJ, Goddard AJH, Eaton MD, Nygaard ET, Angelo PL, Smedley-Stevenson RP, Merton SR, Smith PNet al., 2014,

    The immersed body supermeshing method for modelling reactor physics problems with complex internal structures

    , ANNALS OF NUCLEAR ENERGY, Vol: 63, Pages: 399-408, ISSN: 0306-4549
    Williams DA, O'Brien DP, Schenk PM, Denevi BW, Carsenty U, Marchi S, Scully JEC, Jaumann R, De Sanctis MC, Palomba E, Ammannito E, Longobardo A, Magni G, Frigeri A, Russell CT, Raymond CA, Davison TMet al., 2014,

    Lobate and flow-like features on asteroid Vesta

    , Planetary and Space Science, Vol: 103, Pages: 24-35, ISSN: 0032-0633

    © 2013 Elsevier Ltd. All rights reserved. We studied high-resolution images of asteroid Vesta's surface (~70 and 20-25 m/pixel) obtained during the High- and Low-Altitude Mapping Orbits (HAMO, LAMO) of NASA's Dawn mission to assess the formation mechanisms responsible for a variety of lobate, flow-like features observed across the surface. We searched for evidence of volcanic flows, based on prior mathematical modeling and the well-known basaltic nature of Vesta's crust, but no unequivocal morphologic evidence of ancient volcanic activity has thus far been identified. Rather, we find that all lobate, flow-like features on Vesta appear to be related either to impact or erosional processes. Morphologically distinct lobate features occur in and around impact craters, and most of these are interpreted as impact ejecta flows, or possibly flows of impact melt. Estimates of melt production from numerical models and scaling laws suggests that large craters like Marcia (~60 km diameter) could have potentially produced impact melt volumes ranging from tens of millions of cubic meters to a few tens of cubic kilometers, which are relatively small volumes compared to similar-sized lunar craters, but which are consistent with putative impact melt features observed in Dawn images. There are also examples of lobate flows that trend downhill both inside and outside of crater rims and basin scarps, which are interpreted as the result of gravity-driven mass movements (slumps and landslides).

    Jacobs CT, Collins GS, Piggott MD, Kramer SCet al., 2014,

    Multiphase flow modelling of explosive volcanic eruptions using an adaptive unstructured mesh-based approach

    , Pages: 7406-7417

    Explosive volcanic eruption events, in which large quantities of hot gas and ash are expelled high into the atmosphere, are one of the most powerful natural hazards. In order to gain a full understanding of the dangers these eruptions pose, their complex multiscale and multiphase nature must be captured to a high degree of accuracy. The application of numerical multiphase flow models often represents the only tenable way of achieving this, and permits the investigation of ash cloud evolution in domains many times larger than the laboratory-scale. However, even the most advanced models of eruption dynamics are restricted by the fixed mesh-based approaches that they generally employ. The research presented herein introduces a compressible multiphase flow model recently implemented within Fluidity, a combined finite element / control volume CFD code, for the study of explosive volcanic eruptions. Fluidity adopts an adaptive unstructured mesh-based approach to discretise the domain and focus numerical resolution only in areas important to the dynamics, while decreasing resolution where it is not needed as a simulation progresses. This allows the accurate but economical representation of the flow dynamics throughout time. The application of the model considers a 7 km × 7 km domain in which the violent eruption of hot gas and volcanic ash high into the atmosphere is simulated. It is shown by a convergence analysis that Fluidity offers the same solution accuracy for reduced computational cost using an adaptive unstructured mesh, compared to the same simulation performed with a fixed uniform mesh.

    Lamb AR, Gorman GJ, Elsworth D, 2013,

    A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

    Ciesla FJ, Davison TM, Collins GS, O'Brien DPet al., 2013,

    Thermal consequences of impacts in the early Solar System.

    , Meteoritics and Planetary Science, Vol: 48, Pages: 2559-2567, ISSN: 1086-9379
    Brito-Parada PR, Neethling SJ, Cilliers JJ, 2013,

    Modelling the behaviour of the wetting front in non-standard forced foam drainage scenarios

    Miljkovic K, Wieczorek MA, Collins GS, Laneuville M, Neumann GA, Melosh HJ, Solomon SC, Phillips RJ, Smith DE, Zuber MTet al., 2013,

    Asymmetric Distribution of Lunar Impact Basins Caused by Variations in Target Properties

    , SCIENCE, Vol: 342, Pages: 724-726, ISSN: 0036-8075
    Hassan MHA, Johnson HD, Allison PA, Abdullah WHet al., 2013,

    Sedimentology and stratigraphic development of the upper Nyalau Formation (Early Miocene), Sarawak, Malaysia: A mixed wave- and tide-influenced coastal system

    , JOURNAL OF ASIAN EARTH SCIENCES, Vol: 76, Pages: 301-311, ISSN: 1367-9120
    Xie Z, Lin B, Falconer RA, Maddux TBet al., 2013,

    Large-eddy simulation of turbulent open-channel flow over three-dimensional dunes

    , Journal of Hydraulic Research, Vol: 51, Pages: 494-505, ISSN: 0022-1686

    A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow over three-dimensional (3D) dunes. The governing equations have been discretized using the finite volume method, with the partial cell treatment being implemented in a Cartesian grid form to deal with the 3D dune topography. The simulated free surface elevations, mean flow velocities and Reynolds shear stress distributions have been compared with experimental measurements published in the literature. Relatively close agreement has been obtained between the two sets of results. The predicted mean velocity field and the associated turbulence structure are significantly different from those observed for flows over two-dimensional dunes. The effects of dune three-dimensionality are reflected in spanwise variations of mean flow fields, secondary currents and different distributions of vertical profiles of the double-averaged velocity. Furthermore, large-scale vortical structures, such as spanwise rollers and hairpin-like structures, are predicted in the simulations, with most of them being generated in the concave regions of the 3D dunes. © 2013 International Association for Hydro-Environment Engineering and Research.

    Buchan AG, Pain CC, Fang F, Navon IMet al., 2013,

    A POD reduced-order model for eigenvalue problems with application to reactor physics

    Davison TM, O'Brien DP, Ciesla FJ, Collins GSet al., 2013,

    The early impact histories of meteorite parent bodies

    , Meteoritics and Planetary Science, Vol: 48, Pages: 1894-1918, ISSN: 1086-9379

    We have developed a statistical framework that uses collisional evolution models, shock physics modeling and scaling laws to determine the range of plausible collisional histories for individual meteorite parent bodies. It is likely that those parent bodies that were not catastrophically disrupted sustained hundreds of impacts on their surfaces — compacting, heating, and mixing the outer layers; it is highly unlikely that many parent bodies escaped without any impacts processing the outer few kilometers. The first 10 - 20 Myr were the most important time for impacts, both in terms of the number of impacts and the increase of specific internal energy due to impacts. The model has been applied to evaluate the proposed impact histories of several meteorite parent bodies: up to 10 parent bodies that were not disrupted in the first 100 Myr experienced a vaporizing collision of the type necessary to produce the metal inclusions and chondrules on the CB chondrite parent; around 1 -- 5\% of bodies that were catastrophically disrupted after 12 Myr sustained impacts at times that match the heating events recorded on the IAB/winonaite parent body; more than 75\% of 100 km radius parent bodies which survived past 100 Myr without being disrupted sustained an impact that excavates to the depth required for mixing in the outer layers of the H chondrite parent body; and to protect the magnetic field on the CV chondrite parent body, the crust would have had to have been thick (~ 20 km) in order to prevent it being punctured by impacts.

    Legler B, Johnson HD, Hampson GJ, Massart BYG, Jackson CA-L, Jackson MD, El-Barkooky A, Ravnas Ret al., 2013,

    Facies model of a fine-grained, tide-dominated delta: Lower Dir Abu Lifa Member (Eocene), Western Desert, Egypt

    , SEDIMENTOLOGY, Vol: 60, Pages: 1313-1356, ISSN: 0037-0746
    Kimura S, Candy AS, Holland PR, Piggott MD, Jenkins Aet al., 2013,

    Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves

    , OCEAN MODELLING, Vol: 67, Pages: 39-51, ISSN: 1463-5003
    Latham J-P, Anastasaki E, Xiang J, 2013,

    New modelling and analysis methods for concrete armour unit systems using FEMDEM

    , COASTAL ENGINEERING, Vol: 77, Pages: 151-166, ISSN: 0378-3839
    Goffin MA, Baker CMJ, Buchan AG, Pain CC, Eaton MD, Smith PNet al., 2013,

    Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

    , JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 242, Pages: 726-752, ISSN: 0021-9991
    Oishi Y, Piggott MD, Maeda T, Kramer SC, Collins GS, Tsushima H, Furumura Tet al., 2013,

    Three-dimensional tsunami propagation simulations using an unstructured mesh finite element model

    , JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH, Vol: 118, Pages: 2998-3018, ISSN: 2169-9313
    Fang F, Pain CC, Navon IM, Cacuci DG, Chen Xet al., 2013,

    The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model

    , COMPUTERS & FLUIDS, Vol: 76, Pages: 33-49, ISSN: 0045-7930
    Baker CMJ, Buchan AG, Pain CC, Tollit BS, Goffin MA, Merton SR, Warner Pet al., 2013,

    Goal based mesh adaptivity for fixed source radiation transport calculations

    , ANNALS OF NUCLEAR ENERGY, Vol: 55, Pages: 169-183, ISSN: 0306-4549
    Potter RWK, Kring DA, Collins GS, Kiefer WS, McGovern PJet al., 2013,

    Numerical modeling of the formation and structure of the Orientale impact basin

    , JOURNAL OF GEOPHYSICAL RESEARCH-PLANETS, Vol: 118, Pages: 963-979, ISSN: 2169-9097
    ELSheikh AH, Pain CC, Fang F, Gomes JLMA, Navon IMet al., 2013,

    Parameter estimation of subsurface flow models using iterative regularized ensemble Kalman filter

    Potter RWK, Collins GS, 2013,

    Numerical modeling of asteroid survivability and possible scenarios for the Morokweng crater-forming impact

    , METEORITICS & PLANETARY SCIENCE, Vol: 48, Pages: 744-757, ISSN: 1086-9379
    Merton SR, Buchan AG, Pain CC, Smedley-Stevenson RPet al., 2013,

    An adjoint-based method for improving computational estimates of a functional obtained from the solution of the Boltzmann Transport Equation

    , ANNALS OF NUCLEAR ENERGY, Vol: 54, Pages: 1-10, ISSN: 0306-4549
    Xie Z, 2013,

    Two-phase flow modelling of spilling and plunging breaking waves

    , Applied Mathematical Modelling, Vol: 37, Pages: 3698-3713, ISSN: 0307-904X

    A two-phase flow model, which solves the flow in the air and water simultaneously, has been employed to investigate both spilling and plunging breakers in the surf zone with a focus during wave breaking. The model is based on the Reynolds-averaged Navier-Stokes equations with the k-ε{lunate} turbulence model. The governing equations are solved using the finite volume method, with the partial cell treatment being implemented in a staggered Cartesian grid to deal with complex geometries. The PISO algorithm is utilised for the pressure-velocity coupling and the air-water interface is modelled by the interface capturing method via a high-resolution volume of fluid scheme. Numerical results are compared with experimental measurements and other numerical studies in terms of water surface elevations, mean flow and turbulence intensity, in which satisfactory agreement is obtained. In addition, water surface profiles, velocity and vorticity fields during wave breaking are also presented and discussed. It is shown that the present model is capable of simulating the wave overturning, air entrainment and splash-up processes. © 2012 Elsevier Inc.

    Xiao D, Fang F, Du J, Pain CC, Navon IM, Buchan AG, ElSheikh AH, Hu Get al., 2013,

    Non-linear Petrov-Galerkin methods for reduced order modelling of the Navier-Stokes equations using a mixed finite element pair


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