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Spectral Collocation Methods for One-Dimensional Phase-Change Problems

R. Spall
Journal / Anthology

International Journal of Heat and Mass Transfer
Year: 1995
Volume: 38
Issue: 15
Page range: 2743-2748

Single and multi-domain spectral collocation methods utilizing Chebyshev polynomials were employed to obtain highly accurate solutions to one-dimensional phase-change problems. The Landau transformation was imposed to fix the position of the moving boundary. Spatial derivatives were approximated using both spectral and finite-difference representations. Solutions to the resulting ordinary differential equations in time were obtained using the Gear and Adams predictor-corrector algorithms as implemented within the Mathematica programming environment. For test problems in which exact solutions are available, results for the spectral representations compared favorably with solutions obtained using second-order accurate finite-difference approximations.

*Science > Physics > Thermodynamics and Statistical Mechanics