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On the numerical approach to a two-phase stefan problem with non-linear flux

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Abstract

This paper is devoted to the numerical analysis of a multidimensional two-phase Stefan problem, with a non-linear flux condition on the fixed boundary; the enthalpy formulation is used. A numerical approach suggested by the theory of non-linear semigroup of contractions in L1 (Ω) is introduced; some converging algorithms based on the Crandall-Liggett formula and on the non-linear Chernoff formula are studied. The algebraic non-linear equations are solved by a modified Gauss-Seidel method. The results of several numerical tests are exhibited and discussed.

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  1. Dipartimento di Meccanica Strutturale, Università di Pavia, Via Abbiate-grasso, 27100, Pavia, Italia

    C. Verdi

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  1. C. Verdi
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This work was supported by Ministero Pubblica Istruzione (fondi per la ricerca scientifica) and by Istituto di Analisi Numerica del C.N.R., Pavia.

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Verdi, C. On the numerical approach to a two-phase stefan problem with non-linear flux. Calcolo 22, 351–381 (1985). https://doi.org/10.1007/BF02600382

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