Abstract
Problems of numerical solutions of coupled Stefan and Navier-Stokes equations are analysed. The solvability of stationary problems and the smoothness of their solutions are considered. An iterative method to solve nonlinear equation is proposed. In the method at each iteration step the solution of corresponding linear problem is obtained by means of finite element technique. Estimates for the rate of convergence of the approximate solution to the exact one are given. This method and the estimates are generalized to the case of quasistationary equations. Methods to solve nonstationary problems for Navier-Stokes and Stefan problem are given.
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Rivkind, V. (1991). Numerical solution of coupled Navier-Stokes and Stefan equations. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_4
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DOI: https://doi.org/10.1007/978-3-0348-5715-4_4
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