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.
On the numerical approach to a two-phase Stefan problem with nonlinear flux / C. Verdi. - In: CALCOLO. - ISSN 0008-0624. - 22:3(1985), pp. 351-381. [10.1007/BF02600382]
On the numerical approach to a two-phase Stefan problem with nonlinear flux
C. VerdiPrimo
1985
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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