This paper presents a semi-implicit numerical method for the simulation of grain growth in two dimensions with a multi phase field model. To avoid the strong stability condition of traditional explicit methods, a first-order, semi-implicit discretisation scheme is employed, which offers a good compromise with regard to memory intensity and computational requirements. A nonlinear multigrid solve...

Mechanical properties of metallic materials like steel depend on the solidification process. In order to study the morphology of the microstructure in the materials, the phase-field model derived from the non-equilibrium statistical physics is applied and the interface dynamics is solved by GPU computing. Since very high performance is required, 3-dimensional simulations have not been carried o...

Phase-field models of solidification with convection often assume the existence of a single (mixture) velocity at any location inside the diffuse interface, and the phase-field, φ, is advected by this mixture velocity. In this paper, the advection of the phase-field is examined for a one-dimensional normal flow to a solidification front induced by a density difference between the solid and liqu...

within the effective-field theory with correlations (eft), a transverse random field spin-1 ising model on the simple cubic (z=6) lattice is studied. the phase diagrams, the behavior of critical points, transverse magnetization,  internal energy, magnetic specific heat are obtained numerically and discussed for different values of p the concentration of the random transverse field.