Numerical Analysis of Thermo-electrically Conducting Fluids in a Cubic Cavity Using Vector Finite Element Method for Induction Equations

Abstract

The purpose of this study is to apply vector finite element method to magnetohydrodynamics. Vector finite element method is one of the popular methods in the field of electromagnetism. Two types interpolation functions are defined. One is facet element and another is edge element. In applying vector finite element method to the Inductions equations solenoidal condition is satisfied automatically without iterative corrections. But classical finite element method like B method by Oki et al. needs to solve Poisson equations to satisfy the solenoidal condition. In the present study Induction equations are numerically analyzed with vector finite element method. Flow field and temperature field are analyzed using GSMAC finite element method. We call this analysis technique GSMAC-VFEM (generalized simplified marker and cell vector finite element method). Three-dimensional natural convection in a cavity under a constant magnetic field is analyzed to determine the accuracy and the efficiency of the method. Computational results are compared with B method to verify this numerical scheme. Since the numerical results obtained here agreed well with other numerical results, the new numerical method for solving Induction equations using vector finite element method was verified. Calculation time of new numerical scheme was faster than the other numerical method. The reason is that using vector finite element method for solving Induction equations solenoidal condition for magnetic flux density satisfies automatically.