Non-linear waves of the steady natural convection in a vertical fluid layer: A numerical approach
Mathematics and Computers in Simulation
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In the present work we develop a Galerkin spectral technique for solving coupled higher-order boundary value problems arising in continuum mechanics. The set of the so-called beam functions are used as a basis together with the harmonic functions. As a featuring example we treat the convective flow of a viscous liquid in a vertical slot. We show that the rate of convergence of the series is fifth-order algebraic for the different unknown functions. Though algebraic, the fifth order rate of convergence is fully adequate for the generic problems under consideration, which makes the new technique a useful tool in numerical approaches to convective problems. For a limited range of the governing parameters, we derive asymptotic expansions for the sought functions and find these to be in good agreement with our numerical results.