Modelling of industrial multi-physics processes—a key role for computational mechanics.

In the analysis of industrial processes, there is an increasing emphasis on systems governed by interacting continuum phenomena. Mathematical models of such multi-physics processes can only be achieved for practical simulations through computational solution procedures—computational mechanics. Examples of such multi-physics systems in the context of metals processing are used to explore some of the key issues. Finite-volume methods on unstructured meshes are proposed as a means to achieve efficient rapid solutions to such systems. Issues associated with the software design, the exploitation of high performance computers, and the concept of the virtual computational-mechanics modelling laboratory are also addressed in this context.

The numerical modelling of multi-physics phenomena: The shape casting process

In this paper a computer simulation tool capable of modelling multi-physics processes in complex geometry has been developed and applied to the casting process. The quest for high-quality complex casting components demanded by the aerospace and automobile industries, requires more precise numerical modelling techniques and one that need to be generic and modular in its approach to modelling multi-processes problems. For such a computer model to be successful in shape casting, the complete casting process needs to be addressed, the major events being:-• Filling of hot liquid metal into a cavity mould • Solidification and latent heat evolution of liquid metal • Convection currents generated in liquid metal by thermal gradients • Deformation of cast and stress development in solidified metal • Macroscopic porosity formation The above phenomena combines the analysis of fluid flow, heat transfer, change of phase and thermal stress development. None of these events can be treated in isolation as they inexorably interact with each other in a complex way. Also conditions such as design of running system, location of feeders and chills, moulding materials and types of boundary conditions can all affect on the final cast quality and must be appropriately represented in the model.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Computational modelling of multi-physics processes on high performance parallel computer systems

The demands of the process of engineering design, particularly for structural integrity, have exploited computational modelling techniques and software tools for decades. Frequently, the shape of structural components or assemblies is determined to optimise the flow distribution or heat transfer characteristics, and to ensure that the structural performance in service is adequate. From the perspective of computational modelling these activities are typically separated into: • fluid flow and the associated heat transfer analysis (possibly with chemical reactions), based upon Computational Fluid Dynamics (CFD) technology • structural analysis again possibly with heat transfer, based upon finite element analysis (FEA) techniques.

Discretisation procedures for multi-physics phenomena

Procedures are described for solving the equations governing a multi-physics process. Finite volume techniques are used to discretise, using the same unstructured mesh, the equations of fluid flow, heat transfer with solidification, and solid deformation. These discretised equations are then solved in an integrated manner. The computational mechanics environment, PHYSICA, which facilitates the building of multi-physics models, is described. Comparisons between model predictions and experimental data are presented for the casting of metal components.

Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations

A review of the atomistic modelling of the behaviour of nano-scale structures and processes via molecular dynamics (MD) simulation method of a canonical ensemble is presented. Three areas of application in condensed matter physics are considered. We focus on the adhesive and indentation properties of the solid surfaces in nano-contacts, the nucleation and growth of nano-phase metallic and semi-conducting atomic and molecular films on supporting substrates, and the nano- and multi-scale crack propagation properties of metallic lattices. A set of simulations selected from these fields are discussed, together with a brief introduction to the methodology of the MD simulation. The pertinent inter-atomic potentials that model the energetics of the metallic and semi-conducting systems are also given.

Surface physics at the nano-scale via scanning probe microscopy and molecular dynamics simulations

Probe-based scanning microscopes, such as the STM and the AFM, are used to obtain the topographical and electronic structure maps of material surfaces, and to modify their morphologies on nanoscopic scales. They have generated new areas of research in condensed matter physics and materials science. We will review some examples from the fields of experimental nano-mechanics, nano-electronics and nano-magnetism. These now form the basis of the emerging field of Nano-technology. A parallel development has been brought about in the field of Computational Nano-science, using quantum-mechanical techniques and computer-based numerical modelling, such as the Molecular Dynamics (MD) simulation method. We will report on the simulation of nucleation and growth of nano-phase films on supporting substrates. Furthermore, a theoretical modelling of the formation of STM images of metallic clusters on metallic substrates will also be discussed within the non-equilibrium Keldysh Green function method to study the effects of coherent tunnelling through different atomic orbitals in a tip-sample geometry.

Multi-physics modelling for the fabrication, packaging and reliability of micro-systems components

The latest advances in multi-physics modelling both using high fidelity techniques and reduced order and behavioural models will be discussed. Particular focus will be given to the application and validation of these techniques for modelling the fabrication, packaging and subsequent reliability of micro-systems based components. The paper will discuss results from a number of research projects with particular emphasis on the techniques being developed in a major UK Goverment funded project - 3D-MINTEGRATION (www.3d-mintegration.com).

Choosing the appropriate level of coupling in multi-physics modeling of metallurgical processes

A computational model for the interrelated phenomena in the process of vacuum arc remelting is analyzed and adjusted of optimal accuracy and computation time. The decision steps in this case study are offered as an example how the coupling in models of similar processes can be addressed. Results show dominance of the electromagnetic forces over buoyancy and inertia for the investigated process conditions.

Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.

Dynamics of an axisymmetric electromagnetic ‘crucible’ melting

Different industrial induction melting processes involve free surface and melt-solid interface of the liquid metal subject to dynamic change during the technological operation. Simulation of the liquid metal dynamics requires to solve the non-linear, coupled hydrodynamic-electromagnetic-heat transfer problem accounting for the time development of the liquid metal free boundary with a suitable turbulent viscosity model. The present paper describes a numerical solution method applicable for various axisymmetric induction melting processes, such as, crucible with free top surface, levitation, semi-levitation, cold crucible and similar melting techniques. The presented results in the cases of semi-levitation and crucible with free top surface meltings demonstrate oscillating transient behaviour of the free metal surface indicating the presence of gravity-inertial-electromagnetic waves which are coupled to the internal fluid flow generated by both the rotational and potential parts of the electromagnetic force.

Computational magnetohydrodynamics - Application

There are many processes, particularly in the nuclear and metals processing industries, where electromagnetic fields are used to influence the flow behaviour of a fluid. Procedures exploiting finite volume (FV) methods in both structured and unstructured meshes have recently been developed which enable this influence to be modelled in the context of conventional FV CFD codes. A range of problems have been tackled by the authors, including electromagnetic pumps and brakes, weirs and dams in steelmaking tundishes and interface effects in aluminium smelting cells. Two cases are presented here, which exemplify the application of the new procedures. The first case investigates the influence of electromagnetic fields on solidification front progression in a tin casting and the second case shows how the liquid metals free surface may be controlled through an externally imposed magnetic field in the semi-levitation casting process.

Modelling the adsorption and imaging of C60 molecules on a graphite substrate

The adsorption of a C60 monolayer on a graphite substrate was modelled via molecular dynamics simulation covering a significant period of 160 picoseconds. The final configuration of C60s agrees closely with that observed in a scanning tunnelling microscopy (STM) experiment. Clusters of adsorbed molecules were then selected and their STM-like images were computed via the Keldysh Green function method.