Advanced School PCC02 Centre International des Sciences Mécaniques CISM

CISM Advanced School on
* held on September 2 - 6, 2002   in Udine, Italy

  Coordinated by

  Tomasz Kowalewski & Dominique Gobin


PCC02 photo by P. Adamowicz



The PCC02 School followed PCC99 Workshop, aimed to create a common platform for different groups working on modelling phase change problems. The Workshop addressed both the theoretical bases for the solution of physical and mathematical problems concerning phase changes, and the numerical algorithms necessary for efficient and robust computer implementations. Validation and verification of codes and their implementation to practical industrial situations were given special attention at the meetings. PCC02 should help people working in applied mathematics, numerical modelling and industrial applications to gain knowledge and allow critical assessment of different approaches, numerical methods, physical models and validation methods used in the field.

Phase Change with Convection: modelling and validation

Solid-liquid phase-change phenomena are present in a large number of industrial applications (materials processing, crystal growth, casting of metal - matrix composites, heat storage, food conservation, cryosurgery) and natural processes (iceberg evolution, magma chambers, crust formation). It is generally recognized that the dynamics of such phase change processes are to a large extent influenced by natural convection. Numerical modelling of such strongly non-linear, moving boundary, thermal and fluid flow problems is not a trivial task. Complex flow structures may appear and their sensitivity to small variations of the parameters or boundary and initial conditions imply the use of appropriate physical models and performing numerical methods.
In the case of solidification, the planar interface is generally unstable, creating different structures, such as cells or dendrites. The subsequent growth of dendrites may be analysed by considering the kinetics of solidification and the local heat and mass transfer away from the dendrite tip. A particular issue of recent interest is the effect of convection in the melt on the growth rate and morphology of an isolated dendrite structure. These local mechanisms have drastic consequences at a larger scale and convective motion in the interdendritic melt is a primary cause for a macrosegregation, that is the variation in composition of a solidified alloy for instance. In the microgravity environment, despite the absence of natural convection, problems arising from the effects of Marangoni convection or g-jitter effects seriously damped initial enthusiasm on using space labs for crystal growth.
For these reasons, computer simulation has a major relevance as a tool of analysis of the experimental studies or for the design of engineering hardware. It is first necessary to establish appropriate physical models and then to develop numerical procedures for solving the resulting set of equations. In order to assess a satisfactory level of confidence of the simulation tools, both the model and the procedure have to be tested through properly designed validation experiments, reproducing the basic features of the simulated phenomena. Therefore, besides well-established numerical benchmarks for code verification, experimental benchmarks for code validation have gained a special attention in the recent years, including recent achievements in measurement techniques (optical and electro-optical methods like thermography, tomography or particle image velocimetry). Computer supported experimentation combined with digital processing, digital data recording and data evaluation allows for acquisition of large amount of details on the complex flow structures. They can be used in combination with numerical results to detect, interpret and resolve discrepancies between physical and simulated flow fields.
The aim of the course is to present a review of modelling phase change problems and of recent methods of numerical and experimental analysis used, with a particular focus on solidification coupled to convective flow. Special attention is given to the validation and verification of numerical codes and to the applications to practical problems. Theoretical background and practical examples of tailoring numerical codes will provide framework to develop skills in using them in various branches of physical or engineering problems. The course was addressed to advanced students and scientists from engineering and applied sciences, as well as to physicists and mathematicians interested in the fundamentals of the field. We hope it helped people working on numerical modelling and industrial applications to gain knowledge and allow critical assessment of different numerical approaches, physical models and validation methods used in the field.
T. Kowalewski & D. Gobin

Main topics of the school

PCC02 Publication

  • We are expecting to finish the book containing presentations given during the course by the end of 2002. The book will be distributed through regular channels of CISM publications centre.
  • Participants are encouraged to submit information, web links, example data or full presentations to the PCC02 web page. These submissions are collected under public subdirectory. It can be made restricted to the course participants only upon the author's request. Please submit your material using PCC02 email address: e-mail: The preferable format is PDF, but any format you would like to send is acceptable.







    The archive is intended to be used primarily by the CISM program participants to extend information given during the lectures. The archive may be used for research and educational purposes but the appropriate acknowledgment should be given to the author in any publications that result. Any uses of the archived data must receive written approval from the author.

    Contact us

    Emails regarding PCC02 course, this site, additional submissions, etc... sent to:

    Last modification
    Sept. 11, 2002
    T.A. Kowalewski