Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.
In the paper, the extended finite element method (XFEM) is combined with a recovery procedure in the analysis of the discontinuous Poisson problem. The model considers the weak as well as the strong discontinuity. Computationally efficient low-order finite elements provided good convergence are used. The combination of the XFEM with a recovery procedure allows for optimal convergence rates in the gradient i.e. as the same order as the primary solution. The discontinuity is modelled independently of the finite element mesh using a step-enrichment and level set approach. The results show improved gradient prediction locally for the interface element and globally for the entire domain.
This paper presents the research studies carried out on the application of lattice Boltzmann method (LBM) to computational aeroacoustics (CAA). The Navier-Stokes equation-based solver faces the difficulty of computational efficiency when it has to satisfy the high-order of accuracy and spectral resolution. LBM shows its capabilities in direct and indirect noise computations with superior space-time resolution. The combination of LBM with turbulence models also work very well for practical engineering machinery noise. The hybrid LBM decouples the discretization of physical space from the discretization of moment space, resulting in flexible mesh and adjustable time-marching. Moreover, new solving strategies and acoustic models are developed to further promote the application of LBM to CAA.
A simple analytical method is developed to estimate frequencies of longitudinal modes in closed hard-walled ducts with discontinuities in a cross-sectional area. The approach adopted is based on a general expression for the acoustic impedance for a plane wave motion in a duct and conditions of impedance continuity at duct discontinuities. Formulae for mode frequencies in a form of transcendental equations were found for one, two and three discontinuities in a duct cross-section. An accuracy of the method was checked by a comparison of analytic predictions with calculation data obtained by use of numerical implementation based on the forced oscillator method with a finite difference algorithm.
The Gaussian mixture model (GMM) method is popular and efficient for voice conversion (VC), but it is often subject to overfitting. In this paper, the principal component regression (PCR) method is adopted for the spectral mapping between source speech and target speech, and the numbers of principal components are adjusted properly to prevent the overfitting. Then, in order to better model the nonlinear relationships between the source speech and target speech, the kernel principal component regression (KPCR) method is also proposed. Moreover, a KPCR combined with GMM method is further proposed to improve the accuracy of conversion. In addition, the discontinuity and oversmoothing problems of the traditional GMM method are also addressed. On the one hand, in order to solve the discontinuity problem, the adaptive median filter is adopted to smooth the posterior probabilities. On the other hand, the two mixture components with higher posterior probabilities for each frame are chosen for VC to reduce the oversmoothing problem. Finally, the objective and subjective experiments are carried out, and the results demonstrate that the proposed approach shows greatly better performance than the GMM method. In the objective tests, the proposed method shows lower cepstral distances and higher identification rates than the GMM method. While in the subjective tests, the proposed method obtains higher scores of preference and perceptual quality.
Thermal self-action of an acoustic beam with one discontinuity or several shock fronts is studied in a Newtonian fluid. The stationary self-action of a single sawtooth wave with discontinuity (or some integer number of these waves), symmetric or asymmetric, is considered in the cases of self-focusing and self- defocusing media. The results are compared with the non-stationary thermal self-action of the periodic sound. Thermal self-action of a single shock wave which propagates with the various speeds is considered.
The evaluation accuracies of rock mass structures based on the ratings of the Rock Quality Designation (RQD) and discontinuity spacing (S) in the Rock Mass Rating (RMR) system are very limited due to the inherent restrictions of RQD and S. This study presents an improvement that replaces these two parameters with the modified blockiness index (Bz) in the RMR system. Before proceeding with this replacement, it is necessary for theoretical model building to make an assumption that the discontinuity network contains three sets of mutually orthogonal disc-shaped discontinuities with the same diameter and spacing of discontinuities. Then, a total of 35 types of theoretical DFN (Discrete Fracture Network) models possessing the different structures were built based on the International Society for Rock Mechanics (ISRM) discontinuity classification (ISRM, 1978). In addition, the RQD values of each model were measured by setting the scanlines in the models, and the Bz values were computed following the modified blockiness evaluation method. Correlations between the three indices (i.e., Bz, RQD and S) were explored, and the reliability of the substitution was subsequently verified. Finally, RMR systems based on the proposed method and the standard approach were applied to real cases, and comparisons between the two methods were performed. This study reveals that RQD is well correlated with S but is difficult to relate to the discontinuity diameter (D), and Bz has a good correlation with RQD/S. Additionally, the ratings of RQD and S are always far from the actual rock mass structure, and the Bz ratings are found to give better characterizations of rock mass structures. This substitution in the RMR system was found to be acceptable and practical.