Unclosed Surface Research Articles

Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces

This paper introduces a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or inclusions.

An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction

Complex single/multi-body structures are generally found in ship and ocean engineering. They have the smooth, sharp, concave, and convex surface features in common. Precise modeling of the structures is the basis of numerical simulation. However, the most widely used explicit modeling method requires considerable manual operations. The result is also difficult to reproduce. Therefore, this paper presents a Radial basis function (RBF) based hierarchical (h-) adaptive Cartesian grid method. The RBF is introduced for arbitrary implicit modeling over the Cartesian framework. Thanks to its natural properties, the RBF is easy to use, highly automated, and only needs a set of scatter points for modeling. The block-based h-adaptive mesh refinement (AMR) combined with the RBF aims to enhance the local grid resolution. It accelerates the calculation of intersecting points compared with the uniform Cartesian grid. The accuracy, efficiency, and robustness of the proposed method are validated by the simulation of the 3D analytical ellipsoidal surface and the unclosed conic surface. To select suitable parameters, we thoroughly investigated the uncertainty factors including sample points, RBF functions, and h-AMR grids. The simulation results of the single/multi-body Wigley hull and KCS hull forms verified the proper selection of the factors and the feasibility of our method to solve practical problems.

A finite element method of the self-consistent field theory on general curved surfaces

Block copolymers provide a wonderful platform in the study of soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory (SCFT) has been proven to be a powerful tool for studying the equilibrium ordered structures. Many numerical methods have been developed to solve the SCFT model. However, most of these focus on the bulk systems, and little work on the confined systems, especially on general curved surfaces. In this work, we developed a linear surface finite element method, which has a rigorous mathematical theory to guarantee numerical precision, to study the self-assembled phases of block copolymers on general curved surfaces based on the SCFT. Furthermore, to capture the consistent surface for a given self-assembled pattern, an adaptive approach to optimize the size of the general curved surface has been proposed. To demonstrate the power of this approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces, including five closed surfaces and an unclosed surface. Numerical results illustrate the efficiency of the proposed method. The obtained ordered structures are consistent with the previous results on standard surfaces, such as sphere and torus. More significantly, the proposed numerical framework can be applied to study the phase behaviors of block copolymers on general surfaces accurately.

Effect of Hot Isostatic Pressing and Powder Feedstock on Porosity, Microstructure, and Mechanical Properties of Selective Laser Melted AlSi10Mg

AlSi10Mg tensile bars were additively manufactured using the powder-bed selective laser melting process. Samples were subjected to stress relief annealing and hot isostatic pressing. Tensile samples built using fresh, stored, and reused powder feedstock were characterized for microstructure, porosity, and mechanical properties. Fresh powder exhibited the best mechanical properties and lowest porosity while stored and reused powder exhibited inferior mechanical properties and higher porosity. The microstructure of stress relieved samples was fine and exhibited (001) texture in the z-build direction. Microstructure for hot isostatic pressed samples was coarsened with fainter (001) texture. To investigate surface and interior defects, scanning electron microscopy, optical fractography, and laser scanning microscopy techniques were employed. Hot isostatic pressing eliminated internal pores and reduced the size of surface porosity associated with the selective laser melting process. Hot isostatic pressing tended to increase ductility at the expense of decreasing strength. However, scatter in ductility of hot isostatic pressed parts suggests that the presence of unclosed surface porosity facilitated fracture with crack propagation inward from the surface of the part.

Method of auxiliary sources applied to thin plates and open surfaces

The results of the efficiency study of the Method of Auxiliary Sources (MAS), applied to the problem of electromagnetic wave diffraction by infinitely thin and perfectly conducting unclosed surfaces, are presented in this paper. Planar, corrugated, hemispherical, and half-open surfaces are discussed. The numerical implementation details, allowing the determination of the induced currents on the different sides of the open surface, are discussed. The numerical results obtained with the MAS are compared to those, obtained with the help of the Method of Moments. It is demonstrated that the MAS has some advantages over other methods, is efficient, and trustworthy for the simulation of such problems. This is confirmed by comparing certain numerical results with the real experiment data.

Temporal upscaling of instantaneous evapotranspiration: An intercomparison of four methods using eddy covariance measurements and MODIS data

The quantification of land surface evapotranspiration (ET) at daily or longer time scales is of great significance in modeling the global hydrological cycle, studying climate change, and managing water resources. However, current remote sensing-based ET models can generally only provide snapshots of ET at the time of a satellite overpass and do not satisfy the expectations of hydrologists, irrigation engineers, or water resource managers concerned with practical applications. Four commonly used ET upscaling schemes, namely, the constant reference evaporative fraction (EFr) method, the constant evaporative fraction (EF) method, the constant extraterrestrial solar radiation ratio (R-p) method, and the constant observed global solar radiation ratio (R-g) method, were evaluated in this study using ground-based eddy covariance (EC) measurements and the Moderate Resolution Imaging Spectroradiometer (MODIS) derived estimates from a two-source energy balance model. Analysis was made of both closed and un-closed surface fluxes and of different assumed satellite overpass times from mid-morning to mid-afternoon. Data for the analysis were collected at the Yucheng comprehensive experimental station in Northern China, spanning the period from late April 2009 to late October 2011. The results show that all four upscaling factors from noon to mid-afternoon had a better agreement with their corresponding daily averages. Overall, the EFr (R-g) method had the best (second best) performance of the four upscaling methods. The EF method was found to significantly underestimate the daily latent heat flux (LE) and performed the worst of the four upscaling methods. With the correction of the energy imbalance of EC measurements, the R-g method's performance was improved and outperformed the EF, method in the morning. The presence of clouds either increased or decreased the BIAS but generally increased the root mean square error (RMSE) for all four upscaling methods. When the upscaling methods were applied to convert the instantaneous MODIS remote sensing estimates of ET to daily values, the accuracy of the extrapolated daily ET was controlled by the accuracy of both the remote sensing ET estimates and the upscaling methods themselves. With the insignificantly biased estimates of the instantaneous LE from the N95 model at 101 MODIS overpass times in this study, using the EF method underestimated the daily ET by 11%, while all the remaining three factors overestimated the daily ET by a range of 5%-18%. This study was conducted to provide a scientific basis for developing an operational and more accurate ET-upscaling method with easy access to data in future studies. (C) 2013 Elsevier Inc. All rights reserved.

A sub-grid surface dynamics model for sub-filter surface tension induced interface dynamics

This paper presents a novel model for the sub-filter surface tension induced motion of interfaces separating immiscible fluids. A key feature of the proposed Sub-Grid Surface Dynamics (SGSD) model is to take the sub-filter interface dynamics fully into account by employing a dual-scale approach. Instead of modeling the sub-filter interface geometry, it is resolved on an auxiliary grid using the Refined Level Set Grid approach. The required sub-filter velocity field on the auxiliary grid is reconstructed solving a PDE in a narrow band surrounding the interface. With the fully resolved interface geometry available, the previously unclosed surface tension term in the filtered Navier–Stokes equations can be directly closed using explicit filtering. The novel model shows excellent results for different test cases, including sub-grid oscillations of drops, the sub-grid Rayleigh–Plateau instability, and the viscous capillary breakup of a ligament.

Layered Pentahedral Mesh Generation for Biomechanical Geometries with Unclosed Surfaces

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Application of extended boundary conditions and the Haar wavelets in the analysis of wave scattering by thin screens

A recent approach to solution of 2D scattering problems for electromagnetic waves scattered by thin screens is analyzed. With the use of examples of scattering by a strip and an unclosed cylindrical surface, it is shown that the proposed approach has no advantages in terms of the efficiency of numerical solution over a well-known approach based on exact integral equations for currents that have singular kernels and that are solved with the Krylov-Bogoliubov method.

Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation

The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the com- plex WKB-Maslov method. Analytic asymptotic solutions are constructed in semiclassical approximation in a small parameter ~, ~ ! 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples.

The Nonlinear Schrodinger Equation for a Many-Dimensional System in an Oscillator Field

The method of semi-classical asymptotics is applied to a many-dimensional nonlinear Schrodinger equation with an external anisotropic oscillator field. Solutions asymptotic in a small parameter ħ, ħ → 0, are constructed in the class of functions localized in the neighborhood of an unclosed parabolic surface associated with the phase curve that describes the evolution of the vertex of this surface. In the normal direction to the surface, the functions have the form of the one-soliton solution of a one-dimensional nonlinear Schrodinger equation. The asymptotic evolution operator is considered accurate to O(ħ3/2), ħ → 0, in the specified class of solutions. The phenomenon of collapse is discussed.

General equations with small parameter for the theory of current synthesis on arbitrary nonclosed surfaces

The inverse problem of restoring the space of currents on an arbitrary perfectly conducting surface is solved in the most general form. General equations with small parameter describing the synthesis of currents on arbitrary unclosed surfaces are derived.

Analysis of Electromagnetic Scattering By Open Boundary

An open boundary is an unclosed surface element such as a disk, a hollow pipe of finite length, a hemisphere, and a sum of such surface elements. In this paper, on the basis of the author's rigorous mathematical theory, general algorithms to solve electromagnetic scattering by a metallic open boundary, and also by a non-metallic open boundary, are given, which enable us to solve various important problems in the study of high frequency devices such as antenna, leaky waveguide, grating, etc.

On non-uniqueness of the inverse problem for a seismic source-I. Treatment in terms of equivalent force

SUMMARY The inverse problem of the earthquake-source theory is considered. It is shown that for a seismic source of general type distributed over a 3-D spatial region in infinite homogeneous isotropic elastic medium the problem has no unique solution not only in terms of moment density tensor (Backus & Mulcahy 1976a,b), but also in terms of equivalent force. This fact is related to the existence of non-radiating seismic sources. (A non-radiating seismic source is the one that has non-zero equivalent force but produces no motion outside some ball containing the source region: the acoustic case was considered by Friedlander 1973). We show that in the case when the input data are specified to be the far-field displacements, the only solutions of the homogeneous inverse problem are non-radiating sources. This means that far-field displacements uniquely determine the near-field ones. Therefore, the adding of near-field data cannot improve the statement of the problem to avoid non-uniqueness. To constrain the class of admissible sources we consider 2-D indigenous seismic sources that have a moment density tensor distributed over a known smooth surface. We show that for an unclosed surface the inverse problem has a unique solution in terms of equivalent force. A counter example for the unit sphere shows that if a surface is closed the inverse problem may have no uniqueness.

Theory of nonstationary interaction between pressure waves in a fluid and unclosed surfaces

Problems of nonstationary scattering of incident waves by unclosed surfaces have been solved in the general formulation under the usual assumptions of the linear mechanics of ideal compressible fluids. Such problems are encountered in a number of important hydrodynanic applications. In this case the nonstationary wave field must be known at any distance from the scatterer, and in particular in its immediate vicinity. The known methods of stationary diffraction cannot be used in nonstationary problems, when it is not possible to obtain exact expressions for the Fourier transforms of the unknown solutions and hence guarantee the unique recovery of the inverse transforms. However, the direct solution of the nonstationary problem is possible only in very simple situations: scattering of pressure waves by a plate, diffraction at the edge of a half-plane or at a slit in a flat screen, etc. These circumstances make it necessary to develop special approaches to the solution of the problem of the nonstationary scattering of pressure waves in a fluid by arbitrary unclosed surfaces. This paper outlines a method which leads to the construction of the Laplace transforms of the unknown solutions and is based on a unique means of satisfying the boundary conditions with the subsequent obtaining of exact expressions for the coefficients (densities) of the expansions employed. The class of problems solvable by this method is confined to those for which it is possible to obtain corresponding solutions by expansion in series or integrals over the complete orthogonal system of eigenfunctions on the assumption that the surface of the obstacle is closed. The Laplace transforms of the solutions can be inverted by any approximate method. The solutions constructed in accordance with the formalism developed are in satisfactory agreement with the experimental data and coincide with the classical results.