Research

Over the years I have worked on the computational modelling and analysis of a wide range of materials/metals and minerals processes, including:

• Iron ore pelletisation
• Iron and non-ferrous blast furnaces
• Refractory manufacture
• Continuous casting of steel
• Shape casting of a variety of metals
• Particulate agglomeration
• Particulate comminution
• Sedimentation
• Flocculation
• Direct smelting of iron ores
• Reduction in fluidised beds
• Performance of dental materials in the oral environment
• Magneto-hydrodynamics applied as pumps, brakes, stirrers and in the semi-levitation of metals, heap leaching of minerals, forming and crack propagation in metals

Many of these processes have been essentially multi-physics and multi-scale processes and there have been real challenges in attempting to find effective ways of coupling amongst phenomena and across the time and length scales operating in any given process. Even when a coupling strategy is identified then the compute times can be excessive and so the software has to be effectively implemented on high performance parallel cluster systems. These challenges have been addressed.

Current and recent interests include:

• Computational modelling of ore heap leaching processes
• Iron ore pellet induration
• Centrifugal shape casting for TiAl blades in aerospace engines
• Metal-metal seal design
• Vertical axis wind and water turbine design
• Micro-blood pump design optimisation
• Macro-segregation of metals during solidification
• Multi-physics modelling of the heart function
• Simulation based design of ventilation systems

Selected publications

• D. Carswell, D. McBride, T.N. Croft, A.K. Slone, M. Cross, G. Foster, A CFD model for the prediction of haemolysis in micro axial left ventricular assist devices, Applied Mathematical Modelling, 2013, 37, 6, pp.4199, [ISSN:0307904X], [DOI: 10.1016/j.apm.2012.09.020]
• McBride, D., Mark Cross, Gebhardt, J.E., A Comprehensive Gold Oxide Heap Leach Model: Development And Validation, Hydrometallurgy, 2012, 113-114, pp.98
• Bennett, C.R., McBride, D., Mark Cross, Gebhardt, J.E., A Comprehensive Model for Copper Sulphide Heap Leaching. Part 1 Basic Formulation and Validation Through Column Test Simulation, Hydrometallurgy, 2012, 127-128, pp.150
• David Winfield, Mark Cross, Nick Croft, David Paddison, Geometry optimisation of a gravity dust-catcher using computational fluid dynamics simulation, Chemical Engineering and Processing: Process Intensification, 2012, 62, pp.137, [ISSN:02552701], [DOI: 10.1016/j.cep.2012.08.001]
• C.R. Bennett, D. McBride, M. Cross, J.E. Gebhardt, A comprehensive model for copper sulphide heap leaching, Hydrometallurgy, 2012, 127-128, pp.150, [ISSN:0304386X], [DOI: 10.1016/j.hydromet.2012.08.004]
• Humphreys, N.J., McBride, D.M., Shevchenko, D.M., Croft, T.N., Withey, P., Green, N.R., Mark Cross, Modelling Centrifugal Casting: The Challenges And Validation: International Symposium in Liquid Metals Processing and Casting, Nancy France, September 2011, LMPC Proceedings, LMPC 2011, Proceedings of the 2011 International Symposium on Liquid Metal Processing and Casting, SF2M/CNRS, Paris, France, 2011, pp.297
• Garcia, S., Ramon, C., Esplin, J.E., Gebhardt, A., Hernandez, A., McBride, D., Mark Cross, Gold heap leach simulation and optimization using a multi-physics model, Minerals and Metallurgical Processing, 2010, 27, pp.196
• T.N. Croft, M. Cross, A.K. Slone, A.J. Williams, C.R. Bennett, P. Blot, M. Bannear, R. Jones, CFD analysis of an induration cooler on an iron ore grate-kiln pelletising process, Minerals Engineering, 2009, 22, 9-10, pp.859, [ISSN:08926875], [DOI: 10.1016/j.mineng.2009.03.011]
• T. N. Croft, D. McBride, M. Cross, J. E. Gebhardt, Multi-component free surface flows and rotating devices in the context of minerals processing, International Journal of Computational Fluid Dynamics, 2009, 23, 2, pp.93, [ISSN:1061-85621029-0257], [DOI: 10.1080/10618560902733654]
• D. McBride, T.N. Croft, M. Cross, A coupled finite volume method for the computational modelling of mould filling in very complex geometries, Computers & Fluids, 2008, 37, 2, pp.170, [ISSN:00457930], [DOI: 10.1016/j.compfluid.2007.06.001]
• M. Cross, C.R. Bennett, T.N. Croft, D. McBride, J.E. Gebhardt, Computational modeling of reactive multi-phase flows in porous media: Applications to metals extraction and environmental recovery processes, Minerals Engineering, 2006, 19, 10, pp.1098, [ISBN:0892-6875], [ISSN:08926875], [DOI: 10.1016/j.mineng.2006.05.004]
• D. McBride, M. Cross, N. Croft, C. Bennett, J. Gebhardt, Computational modelling of variably saturated flow in porous media with complex three-dimensional geometries, International Journal for Numerical Methods in Fluids, 2006, 50, 9, pp.1085, [ISBN:0271-2091], [ISSN:0271-20911097-0363], [DOI: 10.1002/fld.1087]
• U Tuzun, J Baxter, H Abou-Chakra, M Cross, M K Patel, N Strusevich, J Wang, N Christakis, P Chapelle, Application of simulation technologies in the analysis of granular material behaviour during transport and storage, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2005, 219, 1, pp.43, [ISBN:0271-2091], [ISSN:0954-40892041-3009], [DOI: 10.1243/095440805X7044]
• G. A. Taylor, C. Bailey, M. Cross, A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics, International Journal for Numerical Methods in Engineering, 2003, 56, 4, pp.507, [ISBN:0029-5981], [ISSN:0029-59811097-0207], [DOI: 10.1002/nme.574]
• Carswell, D., McBride, D., Croft, T.N., Slone, A.K., Mark Cross, Foster, G., A CFD Model for the Prediction of Haemolysis in Micro Axial Left Ventricular Assist Devices, Appl Math Modelling, 0
• Winfield, D., Croft, N., Mark Cross, Paddison, D., Geometry Optimisation Of A Gravity Dust-Catcher Using Computational Fluid Dynamics, 0
• Mark Cross, No title, 0, [DOI: 10.1016/medengphy.2012.12.008]

Teaching

Research theses supervised

PhD

• 2008 - 'Building a software tool simulating the multi-physics of thermal protection systems' (2nd Supervisor: Dr. Thomas Croft)
• 2008 - Computational modelling of glaciological flows (2nd Supervisor: Dr. Thomas Croft)
• 2008 - 'Design of a Miniaturised Implantable Blood Pump/' (2nd Supervisor: Professor Robert Clement)
• 2007 - Computational modelling of Parachute Dynamics in Turbulent Flow (2nd Supervisor: Dr. Avril Slone)
• 2007 - Analysis and optimization of ventilation systems for smoke control through computational fluid dynamics (CFD) modelling (2nd Supervisor: Dr. Christopher Bennett)
• 2006 - Computational modelling of Parachutes. (2nd Supervisor: Professor Paul Tucker)
• 2006 - The Factors Affecting the Performance of Metal to Metal Seals. (2nd Supervisor: Professor Arthur Lees)
• 2005 - The Deterministic modelling of phytoplankton in water supply reservoirs. (2nd Supervisor: Dr. Colin Hayes)

EngD

• 2008 - 'Computational modelling and process analysis of iron blast furnace primary gas cleaning systems' (2nd Supervisor: Dr. Thomas Croft)

MPhil

• 2008 - 'Design of a Miniaturised Implantable Blood Pump/' (2nd Supervisor: Professor Robert Clement)

MRes

• 2008 - Three dimensional multi physics model of the right ventricle of the heart (2nd Supervisor: Dr. Thomas Croft)
• 2007 - Simulating multi physics using the finite volume method (2nd Supervisor: Professor Yuntian Feng)
• 2007 - A numerical model of the glacier midre Lovenbreen (2nd Supervisor: Professor Yuntian Feng)
• 2007 - Computational Modelling of the Tidal Control of Ice Stream Velocities (2nd Supervisor: Professor Yuntian Feng)
• 2006 - CFD Modelling of sediment Transport (2nd Supervisor: Dr. Alison Williams)
• 2006 - MRes Computational Modelling of Parachute Dynamics in Turbulent Flow (2nd Supervisor: Dr. Avril Slone)

Publications

• D. McBride, M. Cross and J E Gebhardt, Heap Leach Modeling Employing CFD Technology: A ‘Process’ Heap Model, Minerals Engineering in press
• D. Carswell, D. McBride, T.N. Croft, A.K. Slone, M. Cross, and G. Foster, A CFD Model for the Prediction of Haemolysis in Micro Axial Left Ventricular Assist Devices, Appl Math Modelling, in press
• C R Bennett, D McBride, M Cross and J E Gebhardt, A Comprehensive Model for Copper Sulphide Heap Leaching. Part 1 Basic Formulation and Validation Through Column Test Simulation, Hydrometallurgy, in press
• D Winfield, N Croft, M Cross And D Paddison, Geometry Optimisation Of A Gravity Dust-Catcher Using Computational Fluid Dynamics, Chemical Engineering & Processing: Process Intensification, in press
• D. McBride, M. Cross and J E Gebhardt, A Comprehensive Gold Oxide Heap Leach Model: Development And Validation, Hydrometallurgy, 113–114, Pages 98-108 (2012)
• A J Williams, A K Slone, T N Croft and M Cross, A mixed Eulerian-Lagrangian method for modelling metal extrusion processes, Computer Methods in Applied Mechanics and Engineering, 199, 2123-2134 (2010)
• M. Willis, I. Masters, S. Thomas, R. Gallie, J. Loman, A. Cook, R. Ahmadian, R. Falconer, B. Lin, G. Gao, M. Cross, N. Croft, A. Williams, M. Muhasilovic, I. Horsfall, R. Fidler, C. Wooldridge, I. Fryett, P. Evans, T. O'Doherty, D. O'Doherty, and A. Mason-Jones. Tidal turbine deployment in the Bristol Channel: a case study, Proceedings of the ICE - Energy, 163, 93-105 (2010)
• M Cross, T N Croft, A K Slone and A J Williams, Computational modelling of
  multi-physics and multi-scale processes in parallel, Journal of Comp Methods in
  Engineering Science and Mechanics, 8, 1-12 (2007)
• A K Slone, T N Croft, A J Williams and M Cross, An alternative mixed
  Eulerian-Lagrangian approach to high speed collision between solid structures
  on parallel clusters, Advances in Engineering Software, 38, 244-255 (2007)
• D McBride, T N Croft and M Cross, Finite volume method for the solution of
  flow on distorted meshes, International Journal of Numerical Methods in Heat
  and Fluid Flow, 17, 213-239 (2007)
• D McBride, T N Croft and M Cross, A coupled finite volume method for the
  solution of flow processes on complex geometries, International Journal of
  Numerical Methods in Fluids, 53, 81-104 (2007)
• Christakis N., P. Chapelle, N. Strusevich, I. Bridle, J. Baxter, M.K.
  Patel, M. Cross, U. Tüzün, A.R. Reed, and M.S.A. Bradley, A hybrid numerical
  model for predicting segregation during core flow discharge, Advances in Powder
  Technology, 17, 641-662 (2006)
• N Christakis, J Wang, M K. Patel, M. S.A. Bradley, M. C. Leaper and M
  Cross, Aggregation and caking processes of granular materials: continuum model
  and numerical simulation with application to sugar, Advances in Powder
  Technology, 17, 543-565 (2006)
• M Cross, K Pericleous, T N Croft, D McBride, J A Lawrence and A J Williams,
  Computational modelling of mold-filling and related free surface flows in shape
  casting: An overview of the challenges involved, Metallurgical & Materials
  Transactions B, 37B, 879-885 (2006)
• M Cross, K Pericleous, G Djambazov and T N Croft, Computational modelling
  of bubbles, droplets and particles in metals reduction and refining, Applied
  Math Modelling, 30, 1445-1458 (2006)
• M Cross, C R Bennett, D McBride, J Gebhardt and D Taylor, Computational
  modelling of primary metal ore heap leaching, Minerals Engineering, 19, 1098-1108 (2006)
• C R Bennett, D McBride, M Cross, J Gebhardt and D Taylor, Simulation
  technology to support primary ore heap leaching, Minerals Processing and
  Extractive Metallurgy, 115, 41-48 (2006)
• A Williams, T N Croft and M Cross, A group based solution strategy for multi-physics simulations in parallel, Applied Math Modelling, 30, 656-674 (2006)
• M Cross, C Bailey, T N Croft, D McBride, K Pericleous, A K Slone and A J
  Williams, Computational Fluid Dynamics: advances in technology for modelling
  iron- and steel- making processes, AIST Transactions, 3, 169-178 (2006)
• D McBride, T N Croft, M Cross, C R Bennett and J Gebhardt, Computational
  modelling of variably saturated flow in porous media with complex three
  dimensional geometries, International Journal of Numerical Methods in Fluids,
  50, 1085-1117 (2006)
• P Chapelle, M Cross and 6 others, Application of simulation technologies in
  the analysis of granular material behaviour during transport and storage, Proc
  IMecheE Part E Journal of Process Mechanical Engineering, 219, 43-52 (2005)
• K McManus, A J Williams, M Cross, T N Croft and C Walshaw, Assessing the
  parallel performance of multi-physics tools for modelling of solidification and
  melting processes, Intl Journal High Perf Comp Applns, 19, 1-27 (2005)
• P Chapelle, M Cross and others, Computational model for prediction of
  particle degradation during dilute- phase pneumatic conveying: the use of a
  laboratory-scale degradation tester for the determination of degradation
  propensity, Advances in Particle Technology, 15, 13-30 (2004)
• P Chapelle, M Cross and others, Computational model for prediction of
  particle degradation during dilute phase pneumatic conveying: Modelling of
  dilute phase pneumatic conveying, Advances in Particle Technology, 15, 31-50 (2004)
• P Chapelle, M Cross and others, Numerical predictions of particle
  degradation in industrial scale pneumatic conveyors, Powder Technology, 143-4,
  321-330 (2004)
• J. Wang, N Christakis, M. K. Patel, M Cross, and M. C. Leaper A
  Computational Model of Coupled Heat and Moisture Transfer with Phase Change in
  Granular Sugar During Varying Environmental Conditions, Numerical Heat Transfer
  A, 45, 751-776 (2004)
• A Mouchmov, M Cross and V. R. Voller, An explicit scheme for coupling
  temperature and concentration fields in solidification models, Applied Math
  Modelling, 28, 79-94 (2004)
• A J Williams, T N Croft and M Cross, Modelling of Ingot Development During
  the Start-up Phase of Direct Chill Casting, Metallurgical and Materials
  Transactions, 34B, 727-734 (2003)
• A K Slone, C Bailey, K Pericleous, M Cross and C Bennett, A Finite Volume
  Unstructured Mesh Approach to Dynamic Fluid-Structure Interaction: An
  Assessment of the challenge of Predicting the Onset of Flutter, Applied Math
  Modelling, 28, 211-239 (2003)
• G Taylor, C Bailey and M Cross, A vertex based finite Volume method applied
  to non-linear material problems in computational solid mechanics, International
  Journal Numerical Methods Engineering, 56, 507-529 (2003)
• A K Slone, C Bailey and M Cross, Dynamic solid mechanics using FV methods,
  Applied Math Modelling, 27, 69-87 (2002)
• S Stoyanov, C Bailey and M Cross, Optimisation modelling for flip-chip
  solder joint reliability, Soldering and Surface Mount Technology, 14, 49-58 (2002)
• A. J. Williams, T. N. Croft and M Cross, Computational Modelling of Metal
  Extrusion and Forging Processes, Journal of Materials Processing Technology, 125-126, 573-582 (2002)
• N Christakis M K Patel, J Baxter, H Abou-Chakra, M Cross and U Tuzun,
  Predictions of Segregation of Granular Material with the aid of PHYSICA, a 3-D
  Unstructured Finite-Volume Modelling Framework, International Journal Numerical
  Methods in Fluids, 40, 281-291 (2002)
• A Slone, K Pericleous, C Bailey and M Cross, Dynamic fluid structure
  interaction using Finite Volume Unstructured Mesh procedures, Computers and
  Structures, 80, 371-390 (2002)

Editorships and advisory positions

• Editor, archival research journal, Applied Mathematical Modelling (published by Elsevier) since 1984
• Editorial board of a number of other journals (including Advances in Engineering Software and the International Journal of Multi-physics)
• Member of the EPSRC College
• Advisor to the DTI Technology Programme
• Reviewer for many international research councils
• Technology consultant to a number of international minerals and metals multi-national corporations

Conferences

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Funding awards

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