The effect of Mo on the microstructure evolution and coarsening kinetics of c0 precipitates in the Ni–Al–Mo system is studied using phase-field simulations with inputs from thermodynamic, kinetic and lattice parameter databases. For alloys of different compositions, the precipitate morphology and the statistical information of precipitate sizes are predicted as a function of annealing time. It ...

Numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formu...

The phenomenon of coarsening has been the topic of intensive study, chiefly in material science, where droplets coalesce1,2 or successive layers of material deposited on a substrate form complex morpholgies3,4. These problems are of technological interest because properties of composite materials such as polymer blends and alloys depend on the size and structure of included droplets5,6; likewis...

Surface growth models may give rise to unstable growth with mound formation whose tipical linear size L increases in time (coarsening process). In one dimension coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models where the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening...

The long time behavior for the degenerate Cahn-Hilliard equation [4, 5, 10], ut = ∇ · (1− u)∇ [Θ 2 {ln(1 + u)− ln(1− u)} − αu− 4u ] , is characterized by the growth of domains in which u(x, t) ≈ u±, where u± denote the ”equilibrium phases;” this process is known as coarsening. The degree of coarsening can be quantified in terms of a characteristic length scale, l(t), where l(t) is prescribed vi...

Algebraic multigrid (AMG) is a very efficient iterative solver and preconditioner for large unstructured linear systems. Traditional coarsening schemes for AMG can, however, lead to computational complexity growth as problem size increases, resulting in increased memory use and execution time, and diminished scalability. Two new parallel AMG coarsening schemes are proposed, that are based on so...

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach...

In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Cen...

Previously we examined the black box multigrid approach to systems of equations. The approach was a direct extension of the methodology used for scalar equations; that is, interpolation and residual weighting were operator induced, and coarsening employed a Galerkin strategy. The application was to standard coarsening of the unknowns. In this paper we consider a semicoarsening approach and find...

Two-dimensional mound coarsening is studied using a continuum model in which the effects of deposition noise have been included but in which coalescence due to mass transfer is assumed to be negligible as expected at low temperature. In agreement with scaling arguments for the case of fluctuation-dominated mound coarsening, we find n = β = 1/3, where n is the mound coarsening exponent and β is ...