Hierarchical Grid Refinement Research Articles

In situ analysis of plastic flow near interfaces and free surfaces

Spatio–temporal analysis of large strain plastic flow at or near interfaces and free surfaces is important for understanding practical problems in the cutting and sliding of metals. In this context, the use of direct in situ imaging, coupled with digital image correlation (DIC), has gained popularity in the past couple of decades since it does not require a priori assumptions about the nature of the deformation field. Moreover, the application of DIC to dynamically evolving interfaces remains challenging. Common techniques such as hierarchical grid refinement or post analysis interpolation are either spatially restrictive or can lead to significant data loss. In this work, we present an alternative experimental method -termed ensemble averaged DIC- that circumvents both these limitations by resorting to ensemble averaging of deformation fields over a number of related, yet independent, unstructured grids. The resulting fields are accurate to second order and are benchmarked against standard 1D and 2D test cases, before being applied to two plastic flow fields arising in deformation processing—frictional sliding and orthogonal machining. We benchmark our scheme against commercially available packages to demonstrate its enhanced ability to resolve plastic flow near interface and free surface. The scheme is shown to accurately estimate residual surface strains on the cut/processed material surface without any a priori information about the flow field.

Analysis of Hierarchical Grid Refinement Techniques for the Lattice Boltzmann Method by Numerical Experiments

Over the last few decades, several grid coupling techniques for hierarchically refined Cartesian grids have been developed to provide the possibility of varying mesh resolution in lattice Boltzmann methods. The proposed schemes can be roughly categorized based on the individual grid transition interface layout they are adapted to, namely cell-vertex or cell-centered approaches, as well as a combination of both. It stands to reason that the specific properties of each of these grid-coupling algorithms influence the stability and accuracy of the numerical scheme. Consequently, this naturally leads to a curiosity regarding the extent to which this is the case. The present study compares three established grid-coupling techniques regarding their stability ranges by conducting a series of numerical experiments for a square duct flow, including various collision models. Furthermore the hybrid-recursive regularized collision model, originally introduced for cell-vertex algorithms with co-located coarse and fine grid nodes, has been adapted to cell-centered and combined methods.

Curvature based feature detection for hierarchical grid refinement in TCAD topography simulations

We present a feature detection method for adaptive grid refinement in hierarchical grids used in process technology computer-aided design topography simulations based on the local curvature of the wafer surface. The proposed feature detection method enables high-accuracy simulations whilst significantly reducing the run-time, because the grid is only refined in areas with high curvatures. We evaluate our feature detection method by simulating selective epitaxial growth of silicon-germanium fins in narrow oxide trenches. The performance and accuracy of the simulation is assessed by comparing the results to experimental data showing good agreement.

3D Multiple Sound Source Localization by Proposed T-Shaped Circular Distributed Microphone Arrays in Combination with GEVD and Adaptive GCC-PHAT/ML Algorithms.

Multiple simultaneous sound source localization (SSL) is one of the most important applications in the speech signal processing. The one-step algorithms with the advantage of low computational complexity (and low accuracy), and the two-step methods with high accuracy (and high computational complexity) are proposed for multiple SSL. In this article, a combination of one-step-based method based on the generalized eigenvalue decomposition (GEVD), and a two-step-based method based on the adaptive generalized cross-correlation (GCC) by using the phase transform/maximum likelihood (PHAT/ML) filters along with a novel T-shaped circular distributed microphone array (TCDMA) is proposed for 3D multiple simultaneous SSL. In addition, the low computational complexity advantage of the GCC algorithm is considered in combination with the high accuracy of the GEVD method by using the distributed microphone array to eliminate spatial aliasing and thus obtain more appropriate information. The proposed T-shaped circular distributed microphone array-based adaptive GEVD and GCC-PHAT/ML algorithms (TCDMA-AGGPM) is compared with hierarchical grid refinement (HiGRID), temporal extension of multiple response model of sparse Bayesian learning with spherical harmonic (SH) extension (SH-TMSBL), sound field morphological component analysis (SF-MCA), and time-frequency mixture weight Bayesian nonparametric acoustical holography beamforming (TF-MW-BNP-AHB) methods based on the mean absolute estimation error (MAEE) criteria in noisy and reverberant environments on simulated and real data. The superiority of the proposed method is presented by showing the high accuracy and low computational complexity for 3D multiple simultaneous SSL.

Multiple Sound Source Localization With Steered Response Power Density and Hierarchical Grid Refinement

Estimation of the direction-of-arrival (DOA) of sound sources is an important step in sound field analysis. Rigid spherical microphone arrays allow the calculation of a compact spherical harmonic representation of the sound field. The standard method for analyzing sound fields recorded using such arrays is steered response power (SRP) maps wherein the source DOA can be estimated as the steering direction that maximizes the output power of a maximally directive beam. This approach is computationally costly since it requires steering the beam in all possible directions. This paper presents an extension to SRP called steered response power density (SRPD) and an associated, signal-adaptive search method called hierarchical grid refinement for reducing the number of steering directions needed for DOA estimation. The proposed method can localize near-coherent as well as incoherent sources while jointly providing the number of prominent sources in the scene. It is shown to be robust to reverberation and additive white noise. An evaluation of the proposed method using simulations and real recordings under highly reverberant conditions as well as a comparison with the state-of-the-art methods are presented.

Trajectory exploration within asynchronous binary asteroid systems using refined Lagrangian coherent structures

Ground observations have found that asynchronous systems constitute most of the population of the near-Earth binary asteroids. This paper concerns the trajectory of a particle in the asynchronous system which is systematically described using periodic ellipsoidal and spherical body models. Due to the non-autonomous characteristics of the asynchronous system, Lagrangian coherent structures (LCS) are employed to identify the various dynamical behaviors. To enhance the accuracy of LCS, a robust LCS finding algorithm is developed incorporating hierarchical grid refinement, one-dimensional search and variational theory verification. In this way, the intricate dynamical transport boundaries are detected efficiently. These boundaries indicate that a total of 15 types of trajectories exist near asynchronous binary asteroids. According to their Kepler energy variations, these trajectories can be grouped into four basic categories, i.e., transitory, escape, impact and flyby trajectories. Furthermore, the influence of the ellipsoid’s spin period on the dynamical behavior is discussed in the context of the change of dynamical regions. We found that the transitory and impact motions occur easily in the synchronous-like binary systems, in which the rotation period of the ellipsoid is nearly equal to that of the mutual orbit. Meanwhile, the results confirm a positive correlation between the spinning rate of the ellipsoid and the probability of the escape and flyby trajectories. The LCS also reveal a marked increase in trajectory diversity after a larger initial energy is selected.

A lattice-Boltzmann method with hierarchically refined meshes

A lattice-Boltzmann method (LBM) with local hierarchical adaptive grid refinement using a cell-centered lattice structure is presented which satisfies the requirements of high accuracy and high efficiency. It is applied to two-dimensional and three-dimensional laminar and turbulent flows over cylinders and spheres which constitute a comprehensive validation of LB methods for such blunt body problems. In the turbulent flow regime, a large-eddy simulation is used to capture the flow physics up to the inertial subrange. The numerical approach is described in detail and the accuracy of the method is demonstrated by considering the flow around a circular cylinder at Reynolds numbers Re=20, 40, and 100 and the flow past a sphere at Re=100, 300, 3700, and 10,000. The LBM plus local hierarchical grid refinement yields accurate temporal and spatial results and dramatically increases the computational efficiency by globally reducing the number of cells.

An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry

Generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries. The paper at hand introduces a B-spline finite element method, which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved. Its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement, which adds several levels of local basis functions in the close vicinity of interfaces, but unfitted to their exact location, so that a simple regular grid of knot span elements can be maintained. Numerical experiments show that an hp-refinement strategy, which simultaneously increases the polynomial degree of the B-spline basis and the levels of refinement around interfaces, achieves exponential rates of convergence despite the presence of discontinuities. It is also demonstrated that the hierarchical B-spline FEM can be used to transfer the recently introduced Finite Cell concept to geometrically nonlinear problems. Its computational performance, imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one, two and three dimensions, and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite.