Employing per-component time step in DSMC simulations of disparate mass and cross-section gas mixtures

A new approach to simulation of stationary flows by Direct Simulation Monte Carlo method is proposed. The idea is to specify an individual time step for each component of a gas mixture. The approach consists of modifications mainly to collision phase and recommendation on choosing time step ratios. It allows softening the demands on the computational resources for cases of disparate collision diameters of molecules and/or disparate molecular masses. These are the cases important in vacuum deposition technologies. Few tests of the new approach are made. Finally, the usage of new approach is demonstrated on a problem of silver nanocluster diffusion in carrier gas argon in conditions of silver deposition experiments.Comment: The goal of submission is to find native English speaker willing to help me polish the paper. This is paper draft sent to Communications in Computational Physics. It is recommended to publication. The need of polishing was one of editors decision. See Additional data for MS Word source fil

On the compatible weakly-nonlocal Poisson brackets of Hydrodynamic Type

We consider the pairs of general weakly non-local Poisson brackets of Hydrodynamic Type (Ferapontov brackets) and the corresponding integrable hierarchies. We show that under the requirement of non-degeneracy of the corresponding "first" pseudo-Riemannian metric $g_{(0)}^{\nu\mu}$ and also some non-degeneracy requirement for the nonlocal part it is possible to introduce a "canonical" set of "integrable hierarchies" based on the Casimirs, Momentum functional and some "Canonical Hamiltonian functions". We prove also that all the "Higher" "positive" Hamiltonian operators and the "negative" symplectic forms have the weakly non-local form in this case. The same result is also true for "negative" Hamiltonian operators and "positive" Symplectic structures in the case when both pseudo-Riemannian metrics $g_{(0)}^{\nu\mu}$ and $g_{(1)}^{\nu\mu}$ are non-degenerate.Comment: 31 Pages, Latex, reference adde

Whitham's Method and Dubrovin-Novikov Bracket in Single-Phase and Multiphase Cases

In this paper we examine in detail the procedure of averaging of the local field-theoretic Poisson brackets proposed by B.A. Dubrovin and S.P. Novikov for the method of Whitham. The main attention is paid to the questions of justification and the conditions of applicability of the Dubrovin-Novikov procedure. Separate consideration is given to special features of single-phase and multiphase cases. In particular, one of the main results is the insensitivity of the procedure of bracket averaging to the appearance of "resonances" which can arise in the multi-phase situation.Comment: 53 pages, extension to the multi-dimensional case is given in arXiv:1211.575