Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: simulation results

[1] Aiki T, Muntean A (2009) Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures. Adv Math Sci Appl 19(1):109–129, MathSciNet Google Scholar
[2] Alecsa CD, Boros I, Frank F, Knabner P, Nechita M, Prechtel A, Rupp A, Suciu N (2020) Numerical benchmark study for flow in heterogeneous aquifers. Adv Water Resour 138:103558. https://doi.org/10.1016/j.advwatres.2020.103558, Article Google Scholar
[3] Casabán M-C, Company R, Jódar L (2023) Numerical difference solution of moving boundary random Stefan problems. Math Comput Simulat 205:878–901. https://doi.org/10.1016/j.matcom.2022.10.026, Article MathSciNet Google Scholar
[4] Cuchiero C, Reisinger C, Rigger S (2024) Implicit and fully discrete approximation of the supercooled Stefan problem in the presence of blow-ups. SIAM J Numer Anal 62(3):1145–1170. https://doi.org/10.1137/22M1509722, Article MathSciNet Google Scholar
[5] Evans JD, King JR (2003) The Stefan problem with nonlinear kinetic undercooling. Q J Mech Appl 56(1):139–161. https://doi.org/10.1093/qjmam/56.1.139, Article MathSciNet Google Scholar
[6] Gupta SC (2003) The classical Stefan problem: basic concepts, modelling and analysis. Elsevier, London. https://doi.org/10.1016/C2017-0-02306-6, Book Google Scholar
[7] Hayes MJ, Park GS (1955) The diffusion of benzene in rubber. Part 1. Low concentrations of benzene. T Faraday Soc 51:1134–1142. https://doi.org/10.1039/TF9555101134, Article Google Scholar
[8] Kaliyathan AV, Rane AV, Jackson S, Thomas S (2021) Analysis of diffusion characteristics for aromatic solvents through carbon black filled natural rubber/butadiene rubber blends. Polym Compos 42:375–396. https://doi.org/10.1002/pc.25832, Article Google Scholar
[9] Kumazaki K, Muntean A (2020) Global weak solvability, continuous dependence on data, and large time growth of swelling moving interfaces. Interf Free Bound 22(1):27–50. https://doi.org/10.4171/ifb/431, Article MathSciNet Google Scholar
[10] Kutluay S, Bahadir AR, Özdeş A (1997) The numerical solution of one-phase classical Stefan problem. J Comput Appl Math 81(1):135–144. https://doi.org/10.1016/S0377-0427(97)00034-4, Article MathSciNet Google Scholar
[11] Lewis PM (1980) Laboratory testing of rubber durability. Polom Test 1:167–189. https://doi.org/10.1016/0142-9418(80)90002-1, Article Google Scholar
[12] Mori M (1976) Stability and convergence of a finite element method for solving the Stefan problem. Publ Res I Math Sci 12(2):539–563. https://doi.org/10.2977/prims/1195190728, Article MathSciNet Google Scholar
[13] Mori M (1977) A finite element method for solving the two phase Stefan problem in one space dimension. Publ Res I Math Sci 13(3):723–753. https://doi.org/10.2977/prims/1195189605, Article MathSciNet Google Scholar
[14] Nepal S, Meyer R, Kröger NH, Aiki T, Muntean A, Wondmagegne Y, Giese U (2021) A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements. KGK-Kaut Gumi Kunst 5:61–69, Google Scholar
[15] Nepal S, Wondmagegne Y, Muntean A (2022) Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber. Int J Numer Anal Mod 19:101–125 (https://global-sci.org/intro/article_detail/ijnam/20351.html), MathSciNet Google Scholar
[16] Nepal S, Ögren M, Wondmagegne Y, Muntean A (2023a) Random walks and moving boundaries: estimating the penetration of diffusants into dense rubbers. Probabilist Eng Mech 74:103546. https://doi.org/10.1016/j.probengmech.2023.103546
[17] Nepal S, Wondmagegne Y, Muntean A (2023b) Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants. Appl Math Comput 442:127733. https://doi.org/10.1016/j.amc.2022.127733
[18] Ögren M (2022) Stochastic solutions of Stefan problems with general time-dependent boundary conditions. In: Malyarenko A, Ni Y, Rančié M, Silvestrov S (eds) Stochastic processes, statistical methods, and engineering mathematics. SPAS 2019, Springer proceedings in mathematics & statistics, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-031-17820-7_29, Chapter Google Scholar
[19] Radu FA, Pop IS, Attinger S (2009) Analysis of an Euler implicit-mixed finite element scheme for reactive solute transport in porous media. Numer Meth Part D E 26(2):320–344. https://doi.org/10.1002/num.20436, Article MathSciNet Google Scholar
[20] Roache PJ (2002) Code verification by the method of manufactured solutions. J Fluids Eng 124(1):4–10. https://doi.org/10.1115/1.1436090, Article Google Scholar
[21] Roy CJ (2005) Review of code and solution verification procedures for computational simulation. J Comput Phys 205:131–156. https://doi.org/10.1016/j.jcp.2004.10.036, Article Google Scholar
[22] Savović S, Caldwell J (2003) Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions. Int J Heat Mass Transf 46(15):2911–2916. https://doi.org/10.1016/S0017-9310(03)00050-4, Article Google Scholar
[23] Stefan J (1891) Über die Theorie der Eisbildung, insbesondere über die Eisbildung im Polarmeere. Ann Physik Chemie 42:269–286. https://doi.org/10.1002/andp.18912780206, Article Google Scholar
[24] Strikwerda JC (2004) Finite difference schemes and partial differential equations. SIAM, London. https://doi.org/10.1137/1.9780898717938, Book Google Scholar
[25] Suciu N (2019) Diffusion in random fields. Applications to transport in groundwater. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-15081-5, Book Google Scholar
[26] Suciu N, Radu FA (2022) Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media. Adv Water Resour 166:104268. https://doi.org/10.1016/j.advwatres.2022.104268, Article Google Scholar
[27] Suciu N, Illiano D, Prechtel A, Radu FA (2021) Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media. Adv Water Resour 152:103935. https://doi.org/10.1016/j.advwatres.2021.103935, Article Google Scholar
[28] Suciu N, Radu FA, Cătinaş E (2024) Iterative schemes for coupled flow and transport in porous media—convergence and truncation errors. Numer Anal Approx Theory 53(1):158–183. https://doi.org/10.33993/jnaat531-1429, Article MathSciNet Google Scholar
[29] Tarzia DA, Turner CV (1997) The one-phase supercooled Stefan problem with a convective boundary condition. Q Appl Math 55(1):41–50. https://doi.org/10.1090/qam/1433750, Article MathSciNet Google Scholar
[30] Tarzia DA, Villa LT (1989) On the free boundary problem in the Wen-Langmuir shrinking core model for noncatalytic gas-solid reactions. Meccanica 24:86–92. https://doi.org/10.1007/BF01560134, Article MathSciNet Google Scholar
[31] Tsunoda K (2015) Derivation of Stefan problem from a one-dimensional exclusion process with speed change. Markov Process Relat 21:263–273, MathSciNet Google Scholar
[32] Visintin A (1996) Models of phase transition. Birkhäuser, London, Google Scholar