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A conservative finite difference scheme for the Falk model system of shape memory alloys
Author(s) -
Yoshikawa Shuji
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300177
Subject(s) - thermoelastic damping , conservation law , entropy (arrow of time) , conservation of energy , scheme (mathematics) , mathematics , first law , statistical physics , computer science , mathematical analysis , thermodynamics , physics , thermal
In this article we propose a new finite difference scheme for the Falk model system. The Falk model system is a thermoelastic system describing the phase transition occurring on shape memory alloys. Our scheme inherits three important properties: the energy conservative law, the momentum conservation law and the law of increasing entropy. In addition, we show the existence of solution for the scheme and positivity of temperature under some conditions.