The paper contains a description of a multiscale algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model. The atomic model uses empirical pair-wise potentials to describe interactions between atoms. The Newton-Raphson method is applied to solve a nanoscale model. The continuum domain is modelled by using BEM. The application of BEM reduces the total number of degrees of freedom in the multiscale model. Some numerical results of simulations at the nanoscale are shown to examine the presented algorithm.
In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidification rate ¶ fS/¶ t (fS Î [0, 1], is a temporary and local volumetric fraction of solid state). The value of fS can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fS can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.
Most researchers have explored noise reduction effects based on the transfer matrix method and the boundary element method. However, maximum noise reduction of a plenum within a constrained space, which frequently occurs in engineering problems, has been neglected. Therefore, the optimum design of multi-chamber plenums becomes essential. In this paper, two kinds of multi-chamber plenums (Case I: a two-chamber plenum that is partitioned with a centre-opening baffle; Case II: a three-chamber plenum that is partitioned with two centre-opening baffles) within a fixed space are assessed. In order to speed up the assessment of optimal plenums hybridized with multiple partitioned baffles, a simplified objective function (OBJ) is established by linking the boundary element model (BEM, developed using SYSNOISE) with a polynomial neural network fit with a series of real data – input design data (baffle dimensions) and output data approximated by BEM data in advance. To assess optimal plenums, a genetic algorithm (GA) is applied. The results reveal that the maximum value of the transmission loss (TL) can be improved at the desired frequencies. Consequently, the algorithm proposed in this study can provide an efficient way to develop optimal multi-chamber plenums for industry.