The research programme I co-ordinate is focused around the development of computational modelling techniques and tools to analyse the transformation and behaviour of materials in manufacturing processes in the context of high performance computing systems. The programme has three highly interactive themes:

• The computational modelling and analysis of materials/minerals/metals processes.
• The development of computational solution procedures and software engineering strategies to address the interacting continuum (sic multi physics and multi-scale) phenomena involved in the above processes.
• The development of tools and strategies to exploit high performance parallel computer (HPPC) systems in this context.

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, the 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.

Current interests include – the computational modelling of ore heap leaching processes, iron ore pellet induration, centrifugal shape casting, parachute modelling, metal-metal seal design, water turbine design, granular coal injection into the blast furnace, macro-segregation of metals during solidification, metals extrusion, ventilation systems, and complex model parameter characterisation.

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.

I have edited the archival research journal, Applied Mathematical Modelling (published by Elsevier) since 1984 and am on the editorial board of a number of other journals (including Advances in Engineering Software and the International Journal of Multi-physics). I am a member of the EPSRC College, an advisor to the DTI Technology Programme, a reviewer for many international research councils and a technology consultant to a number of international minerals and metals multi-national corporations.

I have supervised over 40 PhD students and authored over 350 research publications, including authoring or editing 12 books.

Selected publications since 2001:

2007

• 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
• 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 
• 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
• 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 

2006

• 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.
• 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
• 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 
• 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 
• 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
• 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 
• 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 
• 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
• 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

2005

• 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 
• 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

2004

• 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 
• 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 
• P Chapelle, M Cross and others, Numerical predictions of particle degradation in industrial scale pneumatic conveyors, Powder Technology, 143-4, 321-330 
• 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
• 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

2003

• 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
• 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 
• 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 Num Methods Engineering, 56, 507-529 
• A K Slone, C Bailey and M Cross, Dynamic solid mechanics using FV methods, in 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 
• A. J. Williams, T. N. Croft  and M Cross, Computational Modelling of Metal Extrusion and Forging Processes, Journal of Materials Processing Tech, 125-126, 573-582 
• 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 
• 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  

2001

• P F Leggett, S P Johnson and M Cross, CAPLib—a ‘thin layer’ message passing library to support computational mechanics codes on distributed memory parallel systems, Adv in Engineering Software, 32, 61-83 
• M K Patel, J Haeuser and M Cross, Feature-Oriented Grid Topology Design for Aerospace Configurations, Deutscher Luft- und Raumfahrtkongress, pp:735-743 
• C Walshaw and M Cross, Multilevel Mesh Partitioning for Heterogeneous Communication Networks, Future Generation Computer Systems,17, 601-623 
• C Walshaw and M Cross, Parallel Optimisation Algorithms for Multilevel Mesh Partitioning, Parallel Computing, 26, 1635-1660 
• M. Cross, J. W. Evans and C. Bailey (Editors), Computational Modeling of Materials, Minerals and Metals Processing, TMS, Pennsylvania, ISBN 0 87339 513 1