Two-dimensional Test Research Articles

フラップ式可動ゲートの津波低減性能に関する模型実験

The flap type gate has been developing as storm surge and tsunami countermeasure. Because the flap type gate closes a harbor quickly, it is thought to be effective as a tsunami countermeasure. However, there are some uncertainties in the hydraulic and hydrodynamic characteristics against tsunami. In this paper, two-dimensional hydraulic tests were carried out on the model of scale 1/60 in the water channel with wave maker, and wave pressure and gate behavior of the flap type gate were investigated. As a result, it confirmed that a modified flap type gate was effective as a tsunami countermeasure.

フラップ式水門に作用する段波津波の特性

We have proposed the flap type gate for protection against storm surge and tsunami, and the studies for its hydraulic and hydrodynamic characteristics and design method of it are in progress. In this paper, two-dimensional hydraulic model tests on the scale of 1: 50 were carried out in the flowing water tank with the bore generator, and wave pressure and gate behavior required for designing of the flap type gate were revealed. Besides, function and performance of the flap type gate were examined in terms of disaster prevention against hydraulic bore by tsunami.

A Class of Extended Limiters Applied to Piecewise Hyperbolic Methods

Piecewise hyperbolic methods (PHMs) have been widely used for the approximation of hyperbolic conservation laws. In this paper we have studied the "power limiters" in order to analyze their suitable use in the design of PHMs. We formulate a new PHM, based on these limiters, improving the behavior of the PHM in [SIAM J. Sci. Comput., 15 (1994), pp. 892-915], at local extrema, jump discontinuities, and discontinuities in derivative. We show that this new hyperbolic reconstruction (we call it PowerPHM) is local total variation bounded and it behaves stably with a reduced numerical viscosity compared to PHM. We show numerical evidence of the above mentioned features by means of one- and two-dimensional numerical tests with the Euler equations of gas dynamics.

Critical Heat Flux Experiments on the Reactor Vessel Wall Using 2-D Slice Test Section

The critical heat flux (CHF) on the reactor vessel outer wall was measured using the two-dimensional slice test section. The radius and the channel area of the test section were 2.5 m and 10 cm × 15 cm, respectively. The flow channel area and the heater width were smaller than those of the ULPU experiments, but the radius was greater than that of the ULPU. The CHF data under the inlet subcooling of 2 to 25°C and the mass flux 0 to 300 kg/m2·s had been acquired. The measured CHF value was generally slightly lower than that of the ULPU. The difference possibly comes from the difference of the test section material and the thickness. However, the general trend of CHF according to the mass flux was similar with that of the ULPU. The experimental CHF data were compared with the predicted values by SULTAN correlation. The SULTAN correlation predicted well this study’s data only for the mass flux higher than 200 kg/m2·s, and for the exit quality lower than 0.05. The local condition-based correlation was developed, and it showed good prediction capability for broad quality (-0.01 to 0.5) and mass flux (<300 kg/m2·s) conditions with a root-mean-square error of 2.4%. There were increases in the CHF with trisodium phosphate-added water.

High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids

We present a high-order particle-in-cell (PIC) algorithm for the simulation of kinetic plasmas dynamics. The core of the algorithm utilizes an unstructured grid discontinuous Galerkin Maxwell field solver combining high-order accuracy with geometric flexibility. We introduce algorithms in the Lagrangian framework that preserve the favorable properties of the field solver in the PIC solver. Fast full-order interpolation and effective search algorithms are used for tracking individual particles on the general grid and smooth particle shape functions are introduced to ensure low noise in the charge and current density. A pre-computed levelset distance function is employed to represent the geometry and facilitates complex particle–boundary interaction. To enforce charge conservation we consider two different techniques, one based on projection and one on hyperbolic cleaning. Both are found to work well, although the latter is found be too expensive when used with explicit time integration. Examples of simple plasma phenomena, e.g., plasma waves, instabilities, and Landau damping are shown to agree well with theoretical predictions and/or results found by other computational methods. We also discuss generic well known problems such as numerical Cherenkov radiation and grid heating before presenting a few two-dimensional tests, showing the potential of the current method to handle fully relativistic plasma dynamics in complex geometries.

Strength and signature of force networks in axially compacted sphere and non-sphere granular media: micromechanical investigations

Compaction characteristics of granular materials subjected to axial loading are investigated for both sphere and non-sphere granular assemblies. The computational study is based on the discrete element method (DEM). The compressive stress–strain relation obtained from three-dimensional DEM simulations is compared with that of an idealized two-dimensional plane-strain compression test and physical experiments using a bronze sphere assembly. We observed good agreement between the experimental and three-dimensional DEM simulation results, while two-dimensional simulations significantly underestimate the stiffness of particulate bed, particularly at large strains. This demonstrates that two-dimensional analysis is generally inadequate to model the compaction characteristics of granular systems. We performed a detailed analysis on the force–transmission characteristics of granular materials at microscopic level and present a connection between the directional orientation of force-networks and the invariants of the macroscopic stress tensor: the non-sphere systems were able to build up a strongly anisotropic network of heavily loaded contacts. Several complex phenomena, both geometric and kinematic, that are operative in sphere and non-sphere assemblies due to inter-particle interactions during compression are presented here. It is often assumed that the ratio of invariants of the stress tensor is uniform and constant in uni-axial compression tests. Our results show that the ratio of invariants of the stress tensor is non-uniform and non-constant even when the granular assemblies are subjected to the so-called uni-axial compressive loading, which is in agreement with other recent studies (e.g. Gu et al 2001 Int. J. Plasticity 17 147) performed using the finite element method. The non-homogeneous characteristics that are reported at the particulate scale need to be accounted in considering possible continuum models for the granular systems.

Radon exhalation from phosphogypsum building boards: symmetry constraints, impermeable boundary conditions and numerical simulation of a test case

Comprehensive understanding of 222Rn exhalation from phosphogypsum-bearing building material and its accumulation in indoor air is likely to rely on numerical simulation, particularly if transient effects, three-dimensional domains and convection are to be included and investigated. Yet, experimental data and analytical results are helpful (if not crucial) as far as validation is concerned. Having in mind computational code simplicity and in the light of a recent experimental and theoretical report on 222Rn release from phosphogypsum boards for housing panels, this paper presents and discusses an alternative testing set-up and the corresponding boundary conditions, namely one side of the panel bounded by impermeable wall. Although this is a new facility to be tested, the resultant steady-state one-dimensional diffusion-dominant analytical solution is shown to match the counterpart deduced in the aforementioned previous report, despite it relaxes the constraint of symmetry about the phosphogypsum board centerline, which is inferred in that prior experimental scenario. In addition, numerical results are conducted for a diffusion-dominant two-dimensional time-varying test case concerning 222Rn accumulation in a closed chamber having an exhaling phosphogypsum board tightly placed at one wall.

Application of space–time CE/SE method to shallow water magnetohydrodynamic equations

In this article we apply a space–time conservation element and solution element (CE/SE) method for the approximate solution of shallow water magnetohydrodynamic (SMHD) equations in one and two space dimensions. These equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two-dimensional with magnetic equilibrium in the third direction. In this article we are using a variant of the CE/SE method developed by Zhang et al. [A space–time conservation element and solution element method for solving the two-dimensional unsteady Euler equations using quadrilateral and hexahedral meshes, J. Comput. Phys. 175 (2002) 168–199]. This method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions, respectively. In this method, a single conservation element at each grid point is employed for solving conservation laws no matter in one, two, and three space dimensions. The present scheme use the conservation element to calculate flow variables only, while the gradients of flow variables are calculated by central differencing reconstruction procedure. We give both one- and two-dimensional test computations. A qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution Galerkin schemes. The one- and two-dimensional computations reported in this paper demonstrate the remarkable versatility of the present CE/SE scheme.

Surfactant-enhanced electrokinetic remediation of polycyclic aromatic hydrocarbons in heterogeneous subsurface environments

Polycyclic aromatic hydrocarbon (PAH) contamination exists at numerous sites and poses a substantial risk to public health and the environment. Electrokinetic remediation technology has the potential to treat PAH-contaminated soils, but the effect of soil heterogeneities such as layers, lenses, and mixtures of different soils on the electrokinetic process has not been adequately studied. This study evaluates surfactant-enhanced electrokinetic remediation under heterogeneous soil conditions. A series of bench-scale experiments was conducted using two soils (sand and kaolin) spiked with a representative PAH compound (phenanthrene) in a two-dimensional electrokinetic test apparatus under various layered, lens, or mixed soil configurations. In addition, the homogeneous sand and kaolin soils were each tested alone for comparison purposes. All the experiments employed the same nonionic surfactant (5% Igepal CA-720) flushing solution and a low (0.05) hydraulic gradient. The results showed that the surfactant flushing under the low hydraulic gradient alone was sufficient for complete removal of the contaminant from the homogeneous sand profile, whereas the electroosmotic flow generated by the application of a DC 2.0 V/cm electric potential in a periodic mode considerably enhanced the removal efficiency for the homogeneous and heterogeneous soil profiles containing kaolin. The voltage gradient varied spatially and temporally through the soil profiles and affected the electroosmotic flow and contaminant removal. Key words: clays, electrokinetic remediation, electroosmosis, flushing, heterogeneity, polycyclic aromatic hydrocarbons (PAHs), phenanthrene, soils, sorption, solubilization, surfactants.

Solution Of The Transient Direct Chill CastingProblem With Simultaneous Material AndInterphase Moving Boundaries By The LocalRadial Basis Function Collocation Technique

This paper uses a recently developed upgrade of the classical meshless Kansa method for solution of the transient heat transport in direct-chill casting of aluminium alloys. The problem is characterised by a moving mushy domain between the solid and the liquid phase and a moving starting bottom block that emerges from the mould during the process. The solution of the thermal field is based on the mixture continuum formulation. The movement of the bottom block is approximated by the movement of the boundary condition through the computational domain. The moving domain and boundary of interest are divided into overlapping influence areas. On each of them, the fields are represented by the multiquadrics radial basis function collocation on a related sub-set of nodes. Time-stepping is performed in an explicit way. The governing equation is solved in its strong form, i.e. no integrations are performed. The polygonisation is not present and the method is practically independent on the problem dimension. Realistic boundary conditions and temperature variation of material properties are included. Two-dimensional test case solution is shown at different times, verified by comparison with the finite volume method results.

Iterative solution of a singular convection-diffusion perturbation problem

An iterative domain decomposition method is developed to solve a singular perturbation problem. The problem consists of a convection-diffusion equation with a discontinuous (piecewise-constant) diffusion coefficient, and the problem domain is decomposed into two subdomains, on each of which the coefficient is constant. After showing that the boundary value problem is well posed, we indicate a specific numerical implementation of the iterative technique that combines the finite element method on one subdomain with the method of matched asymptotic expansions on the other subdomain. This procedure extends work by Carlenzoli and Quarteroni, which was originally intended for a boundary layer problem with an outer region and an inner region. Our extension carries over to a problem where the domain consists of the outer and inner boundary layer regions plus a region in which the diffusion coefficient is constant and significant in magnitude. An unexpected benefit of our new implementation is its efficiency, which is due to the fact that at each iteration the problem needs to be solved explicitly only on one subdomain. It is only when the final approximation on the entire domain is desired that the matched asymptotic expansions approximation need be computed on the second subdomain. Two-dimensional convergence results and numerical results illustrating the method for a two-dimensional test problem are given.

Interface tracking with dynamically-redistributed surface markers in unstructured quadrangular grids

In this work we present an extension of a front-tracking algorithm with a dynamical redistribution of surface markers for interface advection of a fluid body in unstructured quadrangular grids. The interface is described by an ordered list of markers connected by segments which are first advected along the streamlines and then redistributed uniformly along the interface while conserving the spanned area. In this article we perform two-dimensional tests over unstructured meshes and compare the results with those obtained in Cartesian grids. Solid body motions, such as translations and rotations, and more complex vortical flows which progressively deform and stretch the interface line are considered over different geometries. The results show that the interface evolution can be tracked successfully in challenging situations with a very good accuracy in terms of area conservation and a rather moderate decrease in the performance of the method with respect to the structured Cartesian mesh.

Application of a photogrammetric technique to a model tunnel

Close range photogrammetric technique (digital imaging process) is a useful non-intrusive method for studying deformation patterns imposing no constraints on the material. In this study, the close range photogrammetric technique for a laboratory two-dimensional model tunnel test using the multi-sized rod material was introduced and consequently, the displacement and strain data were provided to compare with the finite element analysis. The close photogrammetric technique with a linear strain theory showed a remarkable agreement with the physical model data.

Euler–Lagrange equations for the spectral element shallow water system

We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system. We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm.

A dynamic viscoelastic contact problem with normal compliance and damage

We consider a model for dynamic frictionless contact between a viscoelastic body and a foundation. The material constitutive relation is assumed to be nonlinear and the contact is modelled with the normal compliance condition. The mechanical damage of the material, caused by excessive stress or strain, is described by the damage function, the evolution of which is determined by a parabolic inclusion. We derive a variational formulation for the problem and prove the existence of its unique weak solution. We then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions. Finally, we report some numerical results in the simulation of two-dimensional test problems.

Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas

Fluid flow anisotropy in a single rock fracture during a shear process is an important issue in rock mechanics and is investigated in this paper using FEM modelling, considering evolutions of aperture and transmissivity with shear displacement history. The distributions of fracture aperture during shearing with large shear displacements were obtained by numerically manipulating relative translational movements between two digitalized surfaces of a rock fracture replica, with changing sample sizes. The scale dependence of the fluid behaviour and properties were also investigated using a fractal approach. The results show that the fracture aperture increases anisotropically during shear with a more pronounced increase in the direction perpendicular to the shear displacement, causing significant fluid flow channelling effect, as also observed by other researchers. This finding may have important impacts on the interpretation of the results of coupled hydro-mechanical experiments for measurements of hydraulic properties of rock fractures because the hydraulic properties are usually calculated from flow test results along the shear directions while ignoring the more significant anisotropic flow perpendicular to the shear direction. This finding indicates that the coupled stress-flow tests of rough rock fractures should be conducted in true three-dimensions if possible. Significant change in fracture aperture/transmissivity in the out-of-plane direction should be properly evaluated if two-dimensional tests are conducted. Results obtained from numerical simulations also show that fluid flow through a single rough fracture changes with increasing sample size and shear displacements, indicating that representative hydro-mechanical properties of the fractures in the field can only be more reliably determined using samples of large enough sizes beyond the stationarity threshold and tested with larger shear displacements.

Linear and quadratic octahedral wavelets on the sphere for angular discretisations of the Boltzmann transport equation

In this paper, two new wavelet bases are developed for discretising the angular term of the first-order Boltzmann transport equation. The wavelets proposed are based on Sweldens second generation wavelets [Sweldens, W., 1993. The lifting scheme: a construction of second generation wavelets. SIAM J. Math. 1, 54], which are constructed through the lifting procedure [Sweldens, W., 1995. The lifting scheme: a new philosophy in biorthogonal wavelet construction. Wavelet Applications in Signal and Image Processing III]. In this paper, the wavelets are built on an octahedral domain, Fig. 2, and the angular flux approximation takes the form of finite element linear and quadratic representations. Full details of the meshing over the octahedron and derivation of the wavelet functions are given. The wavelets discussed are similar to the wavelets developed in Buchan [Buchan, A., 2003 c. Angular discretisation of the first order Boltzmann transport equation. Part 2: linear spherical wavelets. Technical Report, Imperial College, London, Dep. Earth Sci. Eng.] and [Buchan, A., 2003b. Angular discretisation of the first order Boltzmann transport equation. Part 3: quadratic spherical wavelets. Technical Report, Imperial College, London, Dep. Earth Sci. Eng.], in this paper the bases use a new fundamental amendment for mitigating the inaccuracies observed with the earlier bases. The performance of the new angular discretisation techniques are demonstrated using 2 one-dimensional and 4 two-dimensional test problems. These problems demonstrate the accuracy and susceptibility to ray effects of the proposed methods. Comparisons of all calculations are made with the conventional S N and P N approximations. Benchmark solutions are provided by the established code EVENT.

Indentation testing of human articular cartilage: Effects of probe tip geometry and indentation depth on intra-tissue strain

Experimental determination of intra-tissue deformation during clinically applicable rapid indentation testing would be useful for understanding indentation biomechanics and for designing safe indentation probes and protocols. The objectives of this study were to perform two-dimensional (2-D) indentation tests, using indenters and protocols that are analogous to those in clinically oriented probes, of normal adult-human articular cartilage in order to determine: (1) intra-tissue strain maps and regions of high strain magnitude, and (2) the effects on strain of indenter geometry (rectangular prismatic and cylindrical) and indentation depth (40–190 μm). Epifluorescence microscopy of samples undergoing indentation and subsequent video image correlation analysis allowed determination of strain maps. Regions of peak strain were near the “edges” of indenter contact with the cartilage surface, and the strain magnitude in these regions ranged from ∼0.05 to ∼0.30 in compression and shear, a range with known biological consequences. With increasing indentation displacement, strain magnitudes generally increased in all regions of the tissue. Compared to indentation using a rectangular prismatic tip, indentation with a cylindrical tip resulted in slightly higher peak strain magnitudes while influencing a smaller region of cartilage. These results may be used to refine clinical indenters and indentation protocols.

A variational multiscale higher-order finite element formulation for turbomachinery flow computations

The Variational MultiScale approach for finite elements addresses the inclusion of the effect of fine scales of the solution in the coarse problem. In this framework advective–diffusive–reactive equations modelling turbomachinery flows feature both advection and reaction induced instabilities to be tackled. To this end, this work deals with a new method called V-SGS ( Variable-SubGrid Scale), designed for quadratic elements, with a variable ‘intrinsic time’ parameter. Two-dimensional tests have been considered to compare V-SGS against SUPG and other stabilization devices, including the flow around a NACA 4412 airfoil to assess its reliability in the handling of advanced turbulence closures on cruder meshes.

Ray-chaotic footprints in deterministic wave dynamics: a test model with coupled Floquet-type and ducted-type mode characteristics

Ray chaos, manifested by the exponential divergence of trajectories in an originally thin ray bundle, can occur even in linear electromagnetic propagation environments, due to the inherent nonlinearity of ray-tracing maps. In this paper, we present a novel (two-dimensional) test example of such an environment which embodies intimately coupled refractive wave-trapping and periodicity-induced multiple scattering phenomenologies, and which is amenable to explicit full-wave analysis. Though strictly nonchaotic, it is demonstrated that under appropriate conditions which are inferred from a comprehensive parametric database generated via the above-noted rigorous reference solution, the high-frequency wave dynamics exhibits trends toward irregularity and other peculiar characteristics; these features can be interpreted as "ray-chaotic footprints", and they are usually not observed in geometries characterized by "regular" ray behavior. In this connection, known analogies from other disciplines (particularly quantum physics) are briefly reviewed and related to the proposed test configuration. Moreover, theoretical implications and open issues are discussed, and potential applications are conjectured.