Multi-Incidence Holographic Profilometry for Large Gradient Surfaces with Sub-Micron Focusing Accuracy

Surface reconstruction for micro-samples with large discontinuities using digital holography is a challenge. To overcome this problem, multi-incidence digital holographic profilometry (MIDHP) has been proposed. MIDHP relies on the numerical generation of the longitudinal scanning function (LSF) for reconstructing the topography of the sample with large depth and high axial resolution. Nevertheless, the method is unable to reconstruct surfaces with large gradients due to the need of: (i) high precision focusing that manual adjustment cannot fulfill and (ii) preserving the functionality of the LSF that requires capturing and processing many digital holograms. In this work, we propose a novel MIDHP method to solve these limitations. First, an autofocusing algorithm based on the comparison of shapes obtained by the LSF and the thin tilted element approximation is proposed. It is proven that this autofocusing algorithm is capable to deliver in-focus plane localization with submicron resolution. Second, we propose that wavefield summation for the generation of the LSF is carried out in Fourier space. It is shown that this scheme enables a significant reduction of arithmetic operations and can minimize the number of Fourier transforms needed. Hence, a fast generation of the LSF is possible without compromising its accuracy. The functionality of MIDHP for measuring surfaces with large gradients is supported by numerical and experimental results.

Modelling extreme wave conditions for survivability tests of wave energy converters: CFD versus model tests

<p>This study investigates the experimental and numerical generation of realistic extreme waves in the Model Test Basin (MTB) at the Australian Maritime College, University of Tasmania, in order to test the survivability of offshore structures such as wave energy converters. The sea state and maximum wave height considered were collected during Tropical Cyclone Oma as it tracked down the Queensland Coast of Australia in February 2019. Upon successful generation of a repeatable experimental sample, the NewWave theory was used to regenerate the MTB surface elevation in a STAR-CCM+ computational fluid dynamics (CFD) numerical wave tank. The experimental surface elevation data was analysed with a fast Fourier transform to obtain the wave component amplitudes (a<sub>n</sub>) and phase angles (ε<sub>n</sub>).  These parameters were then used to generate a polychromatic wave in CFD. The 2D CFD simulations were extended to a 3D simulation that included an oscillating water column wave energy converter as per the experimental conditions. Results indicate that experimental focused wave groups can be replicated in CFD software with a similarity of 0.9407 for 2D simulations.  However, by applying an amplification factor to the crest amplitude of the focussed waves, one may further obtain improved accuracy in both 2D and 3D simulations. Further mesh resolution studies surrounding the oscillating water column may improve the accuracy of 3D fluid structure interaction simulations when investigating survivability.</p>

Numerical approximation to Benjamin type equations. Generation and stability of solitary waves

© 2018 Elsevier B.V. This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge–Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves.

Numerical approximation to Benjamin type equations. Generation and stability of solitary waves

© 2018 Elsevier B.V. This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge–Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves.

Effect of the finite size of generated rough surfaces on the percolation threshold

Percolation threshold is a very important parameter to estimate the sealing performance. Thus, it is crucial to determine the correct value of the percolation threshold for contact sealing surfaces. In this paper, we applied a numerical generation method, in which the autocorrelation length can be easily controlled, to obtain different Gaussian isotropic rough surfaces. Then, the contact status between a rigid flat half-space and numerically generated rough surfaces were calculated using the conjugate gradient-fast Fourier transform method. Based on the contact status, the percolation threshold was obtained using a search method. The calculated results established that the percolation threshold of [Formula: see text] is determined for Gaussian isotropic contacting rough surfaces. To obtain an exact value of the percolation threshold, the finite size of the generated rough surfaces should be six times greater than the autocorrelation length, and the autocorrelation length should not be smaller than 20 times the sampling interval.