A novel, particle-based, probabilistic approach for the simulation of cloud microphysics is proposed, which is named the super-droplet method (SDM). This method enables the accurate simulation of cloud microphysics with a less demanding cost in computation. SDM is applied to a warm-cloud system, which incorporates sedimentation, condensation/evaporation and stochastic coalescence. The methodology to couple super-droplets and a non-hydrostatic model is also developed. It is confirmed that the result of our Monte Carlo scheme for the stochastic coalescence of super-droplets agrees fairly well with the solutions of the stochastic coalescence equation. The behaviour of the model is evaluated using a simple test problem, that of a shallow maritime cumulus formation initiated by a warm bubble. Possible extensions of SDM are briefly discussed. A theoretical analysis suggests that the computational cost of SDM becomes lower than the spectral (bin) method when the number of attributes -the variables that identify the state of each superdroplet -becomes larger than some critical value, which we estimate to be in the range 2 ∼ 4.

As a continuation of our efforts to develop efficient and accurate interpolating moving least-squares (IMLS) methods for generating potential energy surfaces, we carry out classical trajectories and compute kinetics properties on higher degree IMLS surfaces. In this study, we have investigated the choice of coordinate system, the range of points (i.e., the cutoff radius) used in fitting, and strategies for selections of data points and basis elements. We illustrate and test the method by applying it to hydrogen peroxide (HOOH). In particular, reaction rates for the O-O bond breaking in HOOH are calculated on fitted surfaces using the classical trajectory approach to test the accuracy of the IMLS method for providing potentials for dynamics calculations.

We performed molecular dynamics simulations of the nucleation of water vapor in order to test nucleation theories. Simulations were performed for a wide range of supersaturation ratios (S = 3-25) and water temperatures (T w = 300-390 K). We obtained the nucleation rates and the formation free energies of a subcritical cluster from the cluster size distribution. The classical nucleation theory and the modified classical nucleation theory (MCNT) overestimate the nucleation rates in all cases. The semi-phenomenological model, which corrects the MCNT prediction using the second virial coefficient of a vapor, reproduces the formation free energy of a cluster with the size 20 to within 10% and the nucleation rate and cluster size distributions to within one order of magnitude. The sticking probability of the vapor molecules to the clusters was also determined from the growth rates of the clusters. The sticking probability rapidly increases with the supersaturation ratio S, which is similar to the Lennard-Jones system. © 2014 AIP Publishing LLC. [http://dx

The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are applied to a six-dimensional potential energy surface (PES) of the HOOH molecule, for which an analytic ("exact") potential is available in the literature. The results of systematic investigations of the effects of weight function parameters, the degree and partial degree of IMLS, the number of data points allowed, and the optimal automatic point selection of data points up to full third-degree IMLS fits are reported. With partial reduction of cross terms and automatic point selection the full six-dimensional HOOH PES can be fit over a range of 100 kcal/mol to an accuracy of less than 1 kcal/mol with approximately 1350 ab initio points.

A new PLIC (piecewise linear interface calculation)-type VOF (volume of fluid) method, called APPLIC (approximated PLIC) method, is presented. Although the PLIC method is one of the most accurate VOF methods, the three-dimensional algorithm is complex. Accordingly, it is hard to develop and maintain the computational code. The APPLIC method reduces the complexity using simple approximation formulae. Three numerical tests were performed to compare the accuracy of the SVOF (simplified volume of fluid), VOF/WLIC (weighed line interface calculation), THINC/SW (tangent of hyperbola for interface capturing/slope weighting), THINC/WLIC, PLIC, and APPLIC methods. The results of the tests show that the APPLIC results are as accurate as the PLIC results and are more accurate than the SVOF, VOF/WLIC, THINC/SW, and THINC/WLIC results. It was demonstrated that the APPLIC method is more computationally efficient than the PLIC method.