Solving two-phase freezing Stefan problems: Stability and monotonicity

• Published in: Mathematical Methods in the Applied Sciences
• Main Authors: Piqueras, Miguel A., Company Rossi, Rafael, Jódar Sánchez, Lucas Antonio
• Other Authors: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Agencia Estatal de Investigación
• Format: Article in Journal/Newspaper
• Language: English
• Published: John Wiley & Sons 2020
• Subjects: Finite difference methods; Non-linear partial differential system; Numerical analysis; Numerical modelling; Two-phase Stefan problem; MATEMATICA APLICADA; Sea ice
• Online Access: http://hdl.handle.net/10251/161982; https://doi.org/10.1002/mma.5787

[EN] The two-phase Stefan problems with phase formation and depletion are special cases ofmoving boundary problemswith interest in science and industry. In this work, we study a solidification problem, introducing a front-fixing transformation. The resulting non-linear partial differential system involves singularities, both at the beginning of the freezing process and when the depletion is complete, that are treated with special attention in the numerical modelling. The problem is decomposed in three stages, in which implicit and explicit finite difference schemes are used. Numerical analysis reveals qualitative properties of the numerical solution spatial monotonicity of both solid and liquid temperatures and the evolution of the solidification front. Numerical experiments illustrate the behaviour of the temperatures profiles with time, as well as the dynamics of the solidification front. Ministerio de Ciencia, Innovacion y Universidades, Grant/Award Number: MTM2017-89664-P. Piqueras, MA.; Company Rossi, R.; Jódar Sánchez, LA. (2020). Solving two-phase freezing Stefan problems: Stability and monotonicity. Mathematical Methods in the Applied Sciences. 43(14):7948-7960. https://doi.org/10.1002/mma.5787 S 7948 7960 43 14 Schmidt, A. (1996). Computation of Three Dimensional Dendrites with Finite Elements. Journal of Computational Physics, 125(2), 293-312. doi:10.1006/jcph.1996.0095 Singh, S., & Bhargava, R. (2014). Simulation of Phase Transition During Cryosurgical Treatment of a Tumor Tissue Loaded With Nanoparticles Using Meshfree Approach. Journal of Heat Transfer, 136(12). doi:10.1115/1.4028730 Company, R., Egorova, V. N., & Jódar, L. (2014). Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing. Abstract and Applied Analysis, 2014, 1-9. doi:10.1155/2014/146745 Griewank, P. J., & Notz, D. (2013). Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage. Journal of Geophysical Research: ...