The coarsening kinetics of a two-phase mixture with a large diffusional mobility disparity between the two phases is studied using a variable-mobility Cahn Hilliard equation. The semi-implicit spectral numerical technique was employed, and a number of interpolation functions are considered for describing the change in diffusion mobility across the interface boundary from one phase to another. The coarsening rate of domain size was measured using both structure and pair correlation functions as well as the direct computation of particle sizes in real space for the case that the coarsening phase consists of dispersed particles. We discovered that the average size (͞R) versus time (t) follows the ͞R^10/3∝t law, in contrast to the conventional LSW theory,͞R³ ∝t, and the interface-diffusion dominated two-phase coarsening, ͞R⁴∝t.

The interaction between free surface flow and structure is investigated using a new level set immersed boundary method. The incorporation of an improved immersed boundary method with a free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving body/bodies of almost arbitrary shape to be modelled. A new algorithm is proposed to locate exact forcing points near solid boundaries, which provides an accurate numerical solution. The discretized linear system of the Poisson pressure equation is solved using the Generalized Minimum Residual (GMRES) method with incomplete LU preconditioning. Uniform flow past a cylinder at Reynolds number Re=100 is modelled using the present model and results agree well with the experiment and numerical data in the literature. Water exit and entry of a cylinder at the prescribed velocity is also investigated. The predicted slamming coefficient is in good agreement with experimental data and previous numerical simulations using a ComFlow model. The vertical slamming force and pressure distribution for the free falling wedge is also studied by the present model and comparisons with available theoretical solutions and experimental data are made.

Structural stability and Si-substitution pattern in fullerene cage of C_60−nSi_n are thoroughly investigated by integrating density functional calculations with a colorbond graph (CBG) model. We find that the parameterized CBG model with genetic algorithms can efficiently scan the large configuration space of alloy and therefore identify the low-energy region within the first-principles accuracy. Low-energy (stable) structures of C_60−nSi_n in carbon-rich region (1≤n≤30) were identified and the silicon atoms are found to tend to aggregate in the fullerene cage. The mixing energy of these low-energy structures is ∼ 35 meV/atom and insensitive to the Si concentration. We expect that these alloy fullerene cages can be synthesized experimentally at elevated temperatures.

We consider the grid resolution necessary to resolve combustion in a mixture of calorically imperfect ideal gases described by detailed kinetics and multicomponent transport. Using the steady premixed laminar flame as a paradigm, the required spatial discretization to capture all detailed physics in the reaction zone is found via 1) determination of the finest grid used in a standard software tool which employs adaptive mesh refinement, 2) examination of peak values of intermediate species mass fractions in the flame zone as a function of grid size, 3) a formal grid resolution study, and 4) a robust new eigenvalue analysis developed to estimate the finest length scale. Application to laminar premixed flames in hydrogen-air flames reveals that the finest length scale is on the order of 10⁻⁴ cm for combustion at atmospheric pressure. Resolution at this scale is shown to be necessary to capture detailed species mass fraction profiles; other features such as steady flame speeds and equilibrium thermochemical properties do not have such a stringent length scale requirement.

The dynamics and interaction of quantized vortices in Bose-Einstein condensates (BECs) are investigated by using the two-dimensional Gross-Pitaevskii equation (GPE) with/without an angular momentum rotation term. If all vortices have the same winding number, they would rotate around the trap center but never collide. In contrast, if the winding numbers are different, their interaction highly depends on the initial distance between vortex centers. The analytical results are presented to describe the dynamics of the vortex centers when β=0. While if β≠0, there is no analytical result but some conclusive numerical findings are provided for the further understanding of vortex interaction in BECs. Finally, the dynamic laws describing the relation of vortex interaction in nonrotating and rotating BECs are presented.

A new stable numerical method, based on Chebyshev wavelets for numerical evaluation of Hankel transform, is proposed in this paper. The Chebyshev wavelets are used as a basis to expand a part of the integrand, r f(r), appearing in the Hankel transform integral. This transforms the Hankel transform integral into a Fourier-Bessel series. By truncating the series, an efficient and stable algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν > −1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθ_i added to the data function f(r), where θ_i is a uniform random variable with values in [−1,1]. Finally, an application of the proposed method is given for solving the heat equation in an infinite cylinder with a radiation condition.

By utilizing a novel quasi-harmonic three-layer dielectric model for the interface between a dielectric spheroid and the surrounding dissimilar dielectric medium, a robust numerical method for calculating the generalized Coulomb and self-polarization potentials of the dielectric spheroid is presented in this paper. The proposed numerical method can not only overcome the inherent mathematical divergence in the self-polarization energy which arises for the simplest step-like model of the dielectric interface, but also completely eliminate the potential numerical divergence which may occur in other treatments. Numerical experiments have demonstrated the convergence of the proposed numerical method as the number of the steps used to discretize the translation layer in a general three-layer dielectric model goes to infinity.

The modified ghost fluid method (MGFM) has been shown to be robust and efficient when being applied to multi-medium compressible flows. In this paper, we rigorously analyze the optimal error estimation of the MGFM when it is applied to the multi-fluid Riemann problem. By analyzing the properties of the MGFM and the approximate Riemann problem solver (ARPS), we show that the interfacial status provided by the MGFM can achieve “third-order accuracy” in the sense of comparing to the exact solution of the Riemann problem, regardless of the solution type. In addition, our analysis further reveals that the ARPS based on a doubled shock structure in the MGFM is suitable for almost any conditions for predicting the interfacial status, and that the “natural” approach of “third-order accuracy” is practically less useful. Various examples are presented to validate the conclusions made.

An implicit high-order accurate method for solving model kinetic equations is proposed. The method is an extension of earlier work on the construction of an explicit TVD method for hybrid unstructured meshes in physical space and is illustrated on the Poiseuille flow of rarefied gas. Examples of calculations are provided for different Knudsen numbers and mesh resolutions, which illustrate the efficiency and high accuracy of the new scheme.

We consider in this paper a high-order, semi-Lagrangian technique to treat possibly degenerate advection-diffusion equations, which has been proposed in similar forms by various authors. The scheme is based on a stochastic representation formula for the solution, which allows to avoid the splitting between advective and diffusive part of the evolution operator. A general theoretical analysis is carried out in the paper, with a special emphasis on the possibility of using large Courant numbers, and numerical tests in one and two space dimensions are presented.