Premium
A control volume capacitance method for solidification modelling with mass transport
Author(s) -
Davey K.,
Rodriguez N. J.
Publication year - 2002
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.405
Subject(s) - control volume , capacitance , thermal conduction , galerkin method , volume (thermodynamics) , finite element method , mechanics , stability (learning theory) , partial differential equation , transient (computer programming) , mathematics , control theory (sociology) , computer science , mathematical analysis , thermodynamics , physics , control (management) , electrode , quantum mechanics , machine learning , artificial intelligence , operating system
Capacitance methods are popular methods used for solidification modelling. Unfortunately, they suffer from a major drawback in that energy is not correctly transported through elements and so provides a source of inaccuracy. This paper is concerned with the development and application of a control volume capacitance method (CVCM) to problems where mass transport and solidification are combined. The approach adopted is founded on theory that describes energy transfer through a control volume (CV) moving relative to the transporting mass. An equivalent governing partial differential equation is established, which is designed to be transformable into a finite element system that is commonly used to model transient heat‐conduction problems. This approach circumvents the need to use the methods of Bubnov–Galerkin and Petrov–Galerkin and thus eliminates many of the stability problems associated with these approaches. An integration scheme is described that accurately caters for enthalpy fluxes generated by mass transport. Shrinkage effects are neglected in this paper as all the problems considered involve magnitudes of velocity that make this assumption reasonable. The CV approach is tested against known analytical solutions and is shown to be accurate, stable and computationally competitive. Copyright © 2002 John Wiley & Sons, Ltd.