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    The Chebyshev Tau Spectral Method for the Solution of the Linear Stability Equations for Rayleigh-Bénard Convection with Melting

    Rubén Avila1, Eduardo Ramos2, S. N. Atluri3

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 73-92, 2009, DOI:10.3970/cmes.2009.051.073

    Abstract A Chebyshev Tau numerical algorithm is presented to solve the perturbation equations that result from the linear stability analysis of the convective motion of a fluid layer that appears when an unconfined solid melts in the presence of gravity. The system of equations that describe the phenomenon constitute an eigenvalue problem whose accurate solution requires a robust method. We solve the equations with our method and briefly describe examples of the results. In the limit where the liquid-solid interface recedes at zero velocity the Rayleigh-Bénard solution is recovered. We show that the critical Rayleigh number Rac and the critical wave… More >

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