Two-dimensional Test Research Articles

A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier–Stokes Equations in Nonhydrostatic Mesoscale Modeling

A discontinuous Galerkin (DG) finite element formulation is proposed for the solution of the compressible Navier-Stokes equations for a vertically stratified fluid, which are of interest in mesoscale nonhydrostatic atmospheric modeling. The resulting scheme naturally ensures conservation of mass, momentum, and energy. A semi-implicit time-integration approach is adopted to improve the efficiency of the scheme with respect to the explicit Runge-Kutta time integration strategies usually employed in the context of DG formulations. A method is also presented to reformulate the resulting linear system as a pseudo-Helmholtz problem. In doing this, we obtain a DG discretization closely related to those proposed for the solution of elliptic problems, and we show how to take advantage of the numerical integration rules (required in all DG methods for the area and flux integrals) to increase the efficiency of the solution algorithm. The resulting numerical formulation is then validated on a collection of classical two-dimensional test cases, including density driven flows and mountain wave simulations. The performance analysis shows that the semi-implicit method is, indeed, superior to explicit methods and that the pseudo-Helmholtz formulation yields further efficiency improvements.

Computational Approaches to Solving Equations Arising from Wound Healing

In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from advection-dominated models of wound healing are solved using four algorithms--MATLAB's inbuilt routine pdepe.m, the Numerical Algorithms Group routine d03pcf.f, and two finite volume methods. The first finite volume method is based on a first-order upwinding treatment of chemotaxis terms and the second on a flux limiting approach. The first test problem admits an analytic solution which can be used to validate the numerical results by analyzing two measures of the error for each method: the average absolute difference and a mass balance error. These criteria as well as the visual comparison between the numerical methods and the exact solution lead us to conclude that flux limiting is the best approach to solving advection-dominated wound healing problems numerically in one dimension. The second test problem is a coupled nonlinear three species model of wound healing angiogenesis. Measurement of the mass balance error for this test problem further confirms our hypothesis that flux limiting is the most appropriate method for solving advection-dominated governing equations in wound healing models. We also consider two two-dimensional test problems arising from wound healing, one that admits an analytic solution and a more complicated problem of blood vessels growth into a devascularized wound bed. The results from the two-dimensional test problems also demonstrate that the flux limiting treatment of advective terms is ideal for an advection-dominated problem.

Binocular Vertical Rectus Muscle Recession For Comitant Vertical Strabismus

Binocular vertical rectus muscle recession has not been formally evaluated in the correction of comitant vertical strabismus. Eight patients with stable comitant vertical strabismus for at least 6 months were included. All underwent recession of the superior rectus muscle of the hypertropic eye combined with an equal or nearly equal recession of the inferior rectus muscle in the hypotropic eye. On the day before surgery, on one of the first three postoperative days, and at one year postoperatively, ocular alignment in vertical and horizontal gaze directions were measured with simultaneous and alternate cover test at a viewing distance of 5 meters, and with the two dimensional Hess screen test. The field of single binocular vision was determined with a Goldmann perimeter. The Lang stereopsis chart was presented at the last follow-up visit. All patients were orthotropic at the last postoperative follow-up visit. In primary gaze, the degree of vertical and horizontal phoria diminished significantly. Normal alignment was achieved in nearly all gaze directions and stereopsis was reestablished. The field of single binocular vision enlarged after the surgery. Binocular vertical rectus muscle recession is an effective surgical approach for patients with comitant vertical ocular misalignment.

Investigating the Lengths of Scale Model Tests to Determine Mean Wave Overtopping Discharges

This paper analyses the influence on the measured mean overtopping discharge of the duration of physical model tests of wave overtopping, bearing in mind the practical purpose of the studies, and the required accuracy of the measurements. The case study of the South Breakwater of Póvoa de Varzim Harbor, Portugal, is used to investigate this subject. During the two-dimensional physical model tests, three main target test conditions were used. For each one, different wave trains were utilized, all conforming to the same target JONSWAP spectrum, and three different test durations were employed. The number of random waves ranged from about 300 to 2400. Then, one of the three main test conditions was again used, but for twelve different test durations. In this case, the number of waves ranged from about 150 to 1900.The results suggest that the convergence of the mean overtopping discharge to a constant value with increasing test duration is not obvious. Regardless of the test duration, the information obtained with a single test gives limited information about the expected mean discharge, as the mean overtopping discharge varies even for the same wave and structure characteristics. Consequently, more information is obtained on the mean discharge if several tests of the same short duration (but with different time series) are undertaken rather than if one test of long duration is carried out.

Theory and operation of 2-D array piezoelectric micromachined ultrasound transducers

Piezoelectric micromachined ultrasound transducers (pMUTs) are a new approach for the construction of 2-D arrays for forward-looking 3-D intravascular (IVUS) and intracardiac (ICE) imaging. Two-dimensional pMUT test arrays containing 25 elements (5 x 5 arrays) were bulk micromachined in silicon substrates. The devices consisted of lead zirconate titanate (PZT) thin film membranes formed by deep reactive ion etching of the silicon substrate. Element widths ranged from 50 to 200 microm with pitch from 100 to 300 mum. Acoustic transmit properties were measured in de-ionized water with a calibrated hydrophone placed at a range of 20 mm. Measured transmit frequencies for the pMUT elements ranged from 4 to 13 MHz, and mode of vibration differed for the various element sizes. Element capacitance varied from 30 to over 400 pF depending on element size and PZT thickness. Smaller element sizes generally produced higher acoustic transmit output as well as higher frequency than larger elements. Thicker PZT layers also produced higher transmit output per unit electric field applied. Due to flexure mode operation above the PZT coercive voltage, transmit output increased nonlinearly with increased drive voltage. The pMUT arrays were attached directly to the Duke University T5 Phased Array Scanner to produce real-time pulse-echo B-mode images with the 2-D pMUT arrays.

A finite-volume ELLAM for non-linear flux convection–diffusion problems

In this paper, a modified finite-volume Eulerian–Lagrangian localized adjoint method (FVELLAM) extended for convection–diffusion problems with a non-linear flux function is introduced. Tracking schemes are discussed using viscous Burgers’ equation. It is shown that in order to have smooth results, only the new time level values should be used in tracking process. Then, the proposed method is employed to study immiscible incompressible two-phase flows in porous media. Various one- and two-dimensional test cases involving internal sources and sinks are solved and accuracy of solution and performance of the method are investigated by comparing the results obtained using FVELLAM with those of fine grid solutions. Finally, it is concluded that although proposed FVELLAM produces satisfactory results even on coarse grids and allows fairly large time-steps, its major advantage is in solving convection-dominated problems in heterogeneous media.

A strategy for the determination of the dielectric permittivity of a lossy soil exploiting GPR surface measurements and a cooperative target

In this paper we deal with an indirect measure of the dielectric permittivity of the soil starting from GPR surface data collected on a buried “cooperative” target, meant as an object buried on purpose and whose extent is known a-priori. This target is exploited in order to achieve, from its image obtained from a suitable GPR data processing, an indirect measure of the dielectric permittivity of the embedding soil. GPR data processing is based on a linear microwave tomographic approach funded on the Born Approximation. Using this Born approach on two-dimensional inversion tests, we investigate the effect of the soil's electrical conductivity and permittivity on this indirect measure and demonstrate that the electrical field scattered by a spot-like buried object permits an accurate estimation of the soil permittivity even when no information of the soil conductivity is available.

Slip parameter estimation of a single wheel using a non-linear observer

SUMMARYSliding mode observer is a variable structure system where the dynamics of a nonlinear system is altered via application of a high-frequency switching control. This paper presents a non-linear sliding mode observer for wheel linear slip and slip angle estimation of a single wheel based on its kinematic model and velocity measurements with added noise to simulate actual on-board sensor measurements. Lyapunov stability theory is used to establish the stability conditions for the observer. It is shown that the observer will converge in a finite time, provided the observer gains satisfy constraints based on a stability analysis. To validate the observer, linear and two-dimensional (2D) test rigs are specially designed. The sliding mode observer is tested under a variety of conditions and it is shown that the sliding mode observer can estimate wheel slip and slip angle to a high accuracy. It is also shown that the sliding mode observer can accurately predict wheel slip and slip angle in the presence of noise, by testing the performance of the sliding mode observer after adding white noise to the measurements. An extended Kalman filter is also developed for comparison purposes. The sliding mode observer is better in terms of prediction accuracy.

Modified Finite Volume Time Domain Method for Efficient Prediction of Radar Cross Section at High Frequencies

The finite volume time domain(FVTD) technique faces serious limitations in simulating electromagnetic scattering at high frequencies due to requirements related to discretization. A modified FVTD method is proposed for electrically large, perfectly conducting scatterers by partially incorporating a time-domain physical optics(PO) approximation for the surface current. Dominant specular returns in the modified FVTD method are modeled using a PO approximation of the surface current allowing for a much coarser discretization at high electrical sizes compared to the original FVTD scheme. This coarse discretization can be based on the minimum surface resolution required for a satisfactory numerical evaluation of the PO integral for the scattered far-field. Non-uniform discretization and spatial accuracy can also be used in the context of the modified FVTD method. The modified FVTD method is aimed at simulating electromagnetic scattering from geometries containing long smooth illuminated sections with respect to the incident wave. The computational efficiency of the modified FVTD method for higher electrical sizes are shown by solving two-dimensional test cases involving electromagnetic scattering from a circular cylinder and a symmetric airfoil.

Wave absorbing system using inclined perforated plates

The interaction of oblique monochromatic incident waves with horizontal/inclined/dual porous plates is investigated in the context of two-dimensional linear potential theory and Darcy's law (the normal velocity of fluid passing through a thin porous plate is linearly proportional to the pressure difference across it). The developed theory is verified by both small-scale and full-scale experiments. First, matched eigenfunction expansion (MEE) solutions for a horizontal porous plate are obtained. The relationship between the plate porosity and the porous parameter is obtained from systematic model tests by using six porous plates with different sizes and spacing of circular holes. Secondly, a multi-domain boundary-element method (BEM) using simple-sources (second-kind modified Bessel function) is developed to confirm the MEE solutions and to apply to more general cases including inclined or multiple porous plates. The BEM-based inner solutions are matched to the eigenfunction-based outer solutions to satisfy the outgoing radiation condition in the far field. Both analytical and BEM solutions with the developed empirical porous parameter agree with each other and correlate well with both small-scale data from a two-dimensional wave-tank test and full-scale measurement in a large wave basin. Using the developed predictive tools, wave-absorption efficiency is assessed for various combinations of porosity, water depth, submergence depth, wave heading, and plate/wave characteristics. In particular, it is found that the performance can be improved by imposing the proper inclination angle near the free surface. The optimal porosity is near porosity P=0.1 and the optimal inclination angle is around 10° as long as the plate length is greater than 20% of the wavelength. Based on the selected optimal parameters (porosity=0.1 and inclination angle=11.3°), the effective wave-absorption system for MOERI's square basin is designed.

Computationally efficient algorithms for the two-dimensional Kolmogorov–Smirnov test

Goodness-of-fit statistics measure the compatibility of random samples against some theoretical or reference probability distribution function. The classical one-dimensional Kolmogorov-Smirnov test is a non-parametric statistic for comparing two empirical distributions which defines the largest absolute difference between the two cumulative distribution functions as a measure of disagreement. Adapting this test to more than one dimension is a challenge because there are 2d-1 independent ways of ordering a cumulative distribution function in d dimensions. We discuss Peacock's version of the Kolmogorov-Smirnov test for two-dimensional data sets which computes the differences between cumulative distribution functions in 4n2 quadrants. We also examine Fasano and Franceschini's variation of Peacock's test, Cooke's algorithm for Peacock's test, and ROOT's version of the two-dimensional Kolmogorov-Smirnov test. We establish a lower-bound limit on the work for computing Peacock's test of Ω(n2lgn), introducing optimal algorithms for both this and Fasano and Franceschini's test, and show that Cooke's algorithm is not a faithful implementation of Peacock's test. We also discuss and evaluate parallel algorithms for Peacock's test.

Wave Overtopping of Póvoa de Varzim Breakwater: Physical and Numerical Simulations

This paper compares the output from four methods used to predict the mean overtopping discharge at the root of the South Breakwater of Povoa de Varzim Harbour (Portugal): two numerical models AMAZON, based on solving the nonlinear shallow-water equations, and COBRAS-UC, based on the Reynolds averaged Navier–Stokes equations, Pedersen’s empirical formula, and the neural network tool NN_Overtopping. Output from the methods is considered alongside data from two-dimensional (2D) physical model tests. The results show that rather accurate predictions can be obtained with COBRAS-UC. Agreement between the data and the AMAZON output depends principally on the impact of porosity on overtopping: agreement is very good when the impact is limited (for high overtopping discharges) and it worsens as porosity plays a more important role (for small discharges). NN_Overtopping estimates the mean discharges with a degree of accuracy similar to AMAZON. Pedersen’s results are those which deviate more from the data, substanti...

Classical and non-classical kinematic fields of two-dimensional penetration tests on granular ground by discrete element method analyses

The penetration test is a widely used in-situ test in geotechnical engineering which mechanism is very important to geomechanics. This paper presents a numerical study on both classic and non-classic kinematic fields in penetration tests on granular ground. A two-dimensional Discrete Element Method (DEM) has been used to simulate penetration tests on a full-size granular ground that is under an amplified gravity and under a K 0 lateral stress boundary. In addition to classical kinematic variables, i.e. displacement and velocity, a non-classical kinematic variable called the average pure rotation rate (APR), which represents particle sizes and particle rotations (M. J. Jiang et al. Kinematic models for non-coaxial granular materials: Part I: theories. Int J Numer Anal Methods Geomech 2005; 29(7): 643–661), is investigated in the penetration test. The DEM numerical results show that the penetration leads to significant changes in displacement, velocity and APR fields, making the soil near the penetrometer move in complex displacement and APR paths. In comparison to velocity field, APR field is very ‘localized’ in the area close to the penetrometer shoulder during penetration. Based on the normalized tip resistance, the penetration process can be described by three phases of penetration, in which the granular ground undergoes three types of failure mechanism, respectively.

Application of Laminar-Turbulent Transition Criteria in Navier-Stokes Computations

A new method concerning laminar-turbulent transition computation was implemented in the ONERA Reynolds-averaged Navier-Stokes solver elsA. It is based on the computation line concept and leads to the removal of most of the mesh topology limitations. Further improvements were also developed, such as the extension of a previous criterion (the Arnal-Habiballah-Delcourt criterion) to separated boundary-layers. Some changes in the numerical treatment of the transition point aimed at stabilizing and improving the accuracy of the computations. Two two-dimensional test cases [the Somers laminar airfoil and the A310 (TC11) profile] and a three-dimensional test case (the variable sweep angle wing) were considered to validate the implementation and the different improvements.

Implementation and analysis of numerical solution of the population balance equation in CFD packages

Simulation of polydisperse flows must include the effects of particle–particle interaction, as breakage and aggregation, coupling the population balance equation (PBE) with the multiphase modelling. In fact, the implementation of efficient and accurate new numerical techniques to solve the PBE is necessary. The direct quadrature method of moments, known as DQMOM, is a moment-based method that uses an optimal adaptive quadrature closure and came into view as a promising choice for this implementation. In the present work, DQMOM was implemented in two CFD packages: the commercial ANSYS CFX, through FORTRAN subroutines, and the open-source OpenFOAM, by directly coding the PBE solution. Transient zero-dimensional and steady one-dimensional simulations were performed in order to explore the PBE solution accuracy using several interpolation schemes. Simulation cases with dominant breakage, dominant aggregation and invariant solution (equivalent breakage and aggregation) were simulated and validated against an analytical solution. The solution of the population balance equation was then coupled to the two-fluid model, considering that all particles classes share the same velocity field. Momentum exchange terms were evaluated using the local instantaneous Sauter mean diameter of the size distribution function. The two-dimensional tests were performed in a backward facing step geometry where the vortex zones traps the particles and provides high rates of breakage and aggregation.

Comparison of 2D fiber network orientation measurement methods

The mechanical properties of tissues, tissue analogs, and biomaterials are dependent on their underlying microstructure. As such, many mechanical models incorporate some aspect of microstructure, but a robust protocol for characterizing fiber architecture remains a challenge. A number of image-based methods, including mean intercept length (MIL), line fraction deviation (LFD), and Fourier transform methods (FTM), have been applied to microstructural images to describe material heterogeneity and orientation, but a performance comparison, particularly for fiber networks, has not been conducted. In this study, we constructed 40 two-dimensional test images composed of simulated fiber networks varying in fiber number, orientation, and anisotropy index. We assessed the accuracy of each method in measuring principal direction (theta) and anisotropy index (alpha). FTM proved to be the superior method because it was more reliable in measurement accuracy (Deltatheta = 2.95 degrees +/- 6.72 degrees , Deltaalpha = 0.03 +/- 0.02), faster in execution time, and flexible in its application. MIL (Deltatheta = 6.23 degrees +/- 10.68 degrees , Deltaalpha = 0.08 +/- 0.06) was not significantly less accurate than FTM but was much slower. LFD (Deltatheta = 9.97 degrees +/- 11.82 degrees , Deltaalpha = 0.24 +/- 0.13) consistently underperformed. FTM results agreed qualitatively with fibrin gel SEM micrographs, suggesting that FTM can be used to obtain image-based statistical measurements of microstructure.

Moving Vortices on the Sphere: A Test Case for Horizontal Advection Problems

Abstract A new two-dimensional advection test on the surface of the sphere is proposed. The test combines a solid-body rotation and a deformational flow field to form moving vortices over the surface of the sphere. The resulting time-dependent deforming vortex centers are located on diametrically opposite sides of the sphere and move along a predetermined great circle trajectory. The horizontal wind field is deformational and nondivergent, and the analytic solution is known at any time. During one revolution around the sphere the initially smooth transported scalar develops strong gradients. Such an approach is therefore more challenging than existing advection test cases on the sphere. To demonstrate the effectiveness and versatility of the proposed test, three different advection schemes are employed, such as a discontinuous Galerkin method on a cubed-sphere mesh, a classical semi-Lagrangian method, and a finite-volume algorithm with adaptive mesh refinement (AMR) on a regular latitude–longitude grid. The numerical results are compared with the analytic solution for different flow orientation angles on the sphere.

Data fusion in automated robotic inspection systems

Teams of small modular inspection vehicles for automated inspection tasks offer the possibility of employing a variety of different NDE inspection methods simultaneously. By synergistically utilising information derived from multiple sources, individual deficiencies and limitations can be partially compensated, leading to a more accurate and precise evaluation of the condition of the engineering structure under test. This paper presents approaches based on fusion of NDE data that have been obtained by a heterogeneous team of small inspection robots which are equipped with payloads for magnetic flux leakage, eddy current and ultrasonic inspection. Any potential uncertainties in individual measurements regarding the location of defects constitute the basis for fusion methods based on statistical and probabilistic algorithms. Images of a two-dimensional test structure have been constructed from data derived from different scans, indicating the positions of detected artificial defects. Applying the Dempster-Shqfer theory of evidence and Bayesian analysis, the confidence level in the accuracy of these images is increased and the uncertainty reduced.

A low diffusion particle method for simulating compressible inviscid flows

A new particle method is presented for the numerical simulation of compressible inviscid gas flows, through procedures which involve relatively small modifications to an existing direct simulation Monte Carlo (DSMC) algorithm. Implementation steps are outlined for simulations involving various grid geometries and for gas mixtures comprising an arbitrary number of species. The proposed method is compared with other numerical schemes through a series of one-dimensional and two-dimensional test cases, and is shown to provide a significant reduction in both artificial diffusion and statistical scatter effects relative to existing DSMC-based equilibrium particle methods.

Experiments on wave transmission coefficients of floating breakwaters

To find a simple, inexpensive, and effective type of floating breakwater for deep-sea aquaculture, we studied three types of structures: the single box, the double box, and the board net. We conducted two-dimensional physical model tests in a wave-current flume in the laboratory to measure the wave transmission coefficients of the three types of breakwaters under regular waves with or without currents. Based on the initial comparison of the wave transmission coefficients, we proposed the use of the board-net floating breakwater for use with fish cages; we then conducted detailed experiments to examine how wave transmission coefficients are affected by several factors, including the width of the board, the row number of the net, the rigidity of the board, and the current velocity. The experimental results show that the board-net floating breakwater, which is a simple and inexpensive type of structure, can effectively protect fish and fish cages and may be adopted for aquaculture engineering in deep-water regions.