Numerical Analysis of Natural Convection of Thermo-Electrically Conducting Fluids in a Square Cavity under a Uniform Magnetic Field : Calculated Results, Frequency Characteristics

Abstract

In our previous research, primitive variable methods were proposed in the numerical scheme of magnetic field of thermo-electrically conducting fluids. The point to be emphasized in the above-mentioned scheme is to satisfy the conservation law of magnetic flux effciently. In the present paper, we compare two numerical schemes of magnetic field, namely the cross helicity method and the numerical residual method, concentrating on the convergence of Poisson's equations of the velocity and magnetic fields. Moreover, the relationship between the periodicity of low Prandtl number fluids and the inhibitory effect of convection due to Lorentz force must be clarified quantitatively. The frequency characteristics of kinetic energy, enstrophy, palinstrophy and hydromagnetic cross helicity are calculated using the maximum entropy method.