Development of the numerical scheme and finite element analysis for thermo-electrically conducting fluids

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The primitive variable methods have been 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 efficiently. In the present research, we have compared the two numerical schemes of magnetic field, namely the cross helicity method and the numerical residual method, concentrating on convergence of Poisson's equation of the velocity and magnetic fields. Moreover, the relationship between the periodicity of low prandtl number fluids and the convective inhibitation effect by Lorentz force has been clarified quantitatively. The frequency characteristics of kinetic energy, enstrophy, palinstrophy and hydromagnetic cross helicity are calculated by the maximum entropy method. Furthermore, we have presented a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method. In order to obtain an optimal shape function, we have introduced an adjoint differential operator to the differential operator for a steady advection-diffusion equation. The shape functions which satisfy these differential operators are mutually dual. One of them interpolates accurately the functions appearing in convection-dominated flows, the other becomes a hybrid-streamlime-upwind weight function. And, we have defined a discrete del operator for the reduction of memory storage in the computer.As a result, we have achieved simplicity of formulation and high-speed calculation of the finite-element method.