A numerical model coupling thermoelectricity, magnetohydrodynamics and dendritic growth

Abstract

The purpose of this paper is to discuss in detail the numerical techniques used to investigate the effects of Thermoelectric Magnetohydrodynamics on dendrtic growth. A numerical model is proposed which couples the growth mechanics, solution to the electric potential, fluid mechanics and the transport of heat and mass. The implementation of the equations, solution techniques and the coupling between each of the various physical phenomena is described. A finite difference sharp interface enthalpy based method is used to solve the evolution of the liquid/solid front. The electric potential becomes the solution to Laplace's equation, with a boundary condition applied to the interface and a sub meshing technique is applied to improve the accuracy. The problem is also inherently 3-dimensional and it can be shown analytically that classical 2-dimensional approximations lead to stagnation of the flow. Therefore a quasi 3-dimensional approximation is used which effectively allows simulations to be carried out in 2-dimensions, which significantly reduces the computational time required.