Premium
Modeling binary alloy solidification by a random projection method
Author(s) -
Carpy Sabrina,
Mathis Hélène
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22322
Subject(s) - liquidus , solidus , projection (relational algebra) , mathematics , phase diagram , projection method , stability (learning theory) , convergence (economics) , boundary value problem , boundary (topology) , numerical analysis , binary number , mathematical analysis , phase (matter) , dykstra's projection algorithm , mathematical optimization , alloy , materials science , algorithm , computer science , physics , metallurgy , economic growth , arithmetic , quantum mechanics , machine learning , economics
This paper addresses the numerical modeling of the solidification of a binary alloy that obeys a liquidus–solidus phase diagram. In order to capture the moving melting front, we introduce a Lagrange projection scheme based on a random sampling projection. Using a finite volume formulation, we define accurate numerical fluxes for the temperature and concentration fields which guarantee the sharp treatment of the boundary conditions at the moving front, especially the jump of the concentration according to the liquidus–solidus diagram. We provide some numerical illustrations which assess the good behavior of the method: maximum principle, stability under CFL condition, numerical convergence toward self‐similar solutions, ability to handle two melting fronts.