In this paper, we propose a phase-field-based spectral element method by solving the Navier–Stokes/Cahn–Hilliard equations for incompressible two-phase flows. With use of Newton–Raphson Cahn–Hilliard equation and time-stepping scheme Navier–Stokes equation, construct three constant (time-independent) coefficient matrixes solutions velocity, pressure, phase variable. Moreover, invoke modified bu...

in this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic ising system consisting of magnetic atoms with spin-1. this study is done using the effectivefield theory (eft) with correlations method. the equations are derived using...

Solidification is an important process in many alloy processing routes. The solidified microstructure of alloys usually made up dendrites, eutectics or a combination both. evolving morphologies are largely determined by the solidification and thus materials properties dependent on conditions. While growth either type well-investigated, there little information coupled both microstructures. This...