@inproceedings{fa01b405a2bc4b6da3068ec62d2f46b4,
title = "A discrete-operator interpolation solution of the phase-field model",
abstract = "Discrete-operator interpolation (DOI) is a numerical technique for computing the function values not computed on the original grid points of a finite-difference (or finite element) scheme. It relys on both the governing equation of the function values and the function values computed on the original grid obtained by using any typical numerical method. This paper applies discrete-operator interpolation for solving the one-dimensional phase-field model applied to melt-front tracking. Our use of DOI for solving the phase-field model serves two purposes. First, we demonstrate that DOI provides a way to construct a numerical solution that is more accurate than the solutions obtained by using a basic numerical method. Second, DOI provides a way to produce solution values at coordinate locations not included in the original set of grid points; this is valuable in many complex numerical simulations. In this paper, we describe the phase- field model together with the details of the discrete-operator interpolation method and their numerical implementations. The results of the phase-field model are obtained using a standard finite-difference (Crank-Nicolson) scheme. DOI results are then compared with these to demonstrate the advantages of this new method.",
author = "Ying Xu and Tianliang Yang and McDonough, {J. M.} and Tagavi, {Kaveh A.}",
year = "2002",
doi = "10.2514/6.2002-3205",
language = "English",
isbn = "9781624101182",
series = "8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference",
booktitle = "8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference",
note = "8th AIAA/ASME Joint Thermophysics and Heat Transfer Conference 2002 ; Conference date: 24-06-2002 Through 26-06-2002",
}