Numerical modelling of two-way propagation of non-linear dispersive waves

We describe and implement a fully discrete spectral method for the numerical solution of a class of non-linear, dispersive systems of Boussinesq type, modelling two-way propagation of long water waves of small amplitude in a channel. For three particular systems, we investigate properties of the numerically computed solutions; in particular we study the generation and interaction of approximate solitary waves.

High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Numerical study of a M-cycle cross-flow heat exchanger for indirect evaporative cooling

In this paper, numerical analyses of the thermal performance of an indirect evaporative air cooler incorporating a M-cycle cross-flow heat exchanger has been carried out. The numerical model was established from solving the coupled governing equations for heat and mass transfer between the product and working air, using the finite-element method. The model was developed using the EES (Engineering Equation Solver) environment and validated by published experimental data. Correlation between the cooling (wet-bulb) effectiveness, system COP and a number of air flow/exchanger parameters was developed. It is found that lower channel air velocity, lower inlet air relative humidity, and higher working-to-product air ratio yielded higher cooling effectiveness. The recommended average air velocities in dry and wet channels should not be greater than 1.77 m/s and 0.7 m/s, respectively. The optimum flow ratio of working-to-product air for this cooler is 50%. The channel geometric sizes, i.e. channel length and height, also impose significant impact to system performance. Longer channel length and smaller channel height contribute to increase of the system cooling effectiveness but lead to reduced system COP. The recommend channel height is 4 mm and the dimensionless channel length, i.e., ratio of the channel length to height, should be in the range 100 to 300. Numerical study results indicated that this new type of M-cycle heat and mass exchanger can achieve 16.7% higher cooling effectiveness compared with the conventional cross-flow heat and mass exchanger for the indirect evaporative cooler. The model of this kind is new and not yet reported in literatures. The results of the study help with design and performance analyses of such a new type of indirect evaporative air cooler, and in further, help increasing market rating of the technology within building air conditioning sector, which is currently dominated by the conventional compression refrigeration technology.

Effect of shear rupture on aggregate scale formation in sea ice

A discrete element model is used to study shear rupture of sea ice under convergent wind stresses. The model includes compressive, tensile, and shear rupture of viscous elastic joints connecting floes that move under the action of the wind stresses. The adopted shear rupture is governed by Coulomb’s criterion. The ice pack is a 400 km long square domain consisting of 4 km size floes. In the standard case with tensile strength 10 times smaller than the compressive strength, under uniaxial compression the failure regime is mainly shear rupture with the most probable scenario corresponding to that with the minimum failure work. The orientation of cracks delineating formed aggregates is bimodal with the peaks around the angles given by the wing crack theory determining diamond-shaped blocks. The ice block (floe aggregate) size decreases as the wind stress gradient increases since the elastic strain energy grows faster leading to a higher speed of crack propagation. As the tensile strength grows, shear rupture becomes harder to attain and compressive failure becomes equally important leading to elongation of blocks perpendicular to the compression direction and the blocks grow larger. In the standard case, as the wind stress confinement ratio increases the failure mode changes at a confinement ratio within 0.2–0.4, which corresponds to the analytical critical confinement ratio of 0.32. Below this value, the cracks are bimodal delineating diamond shape aggregates, while above this value failure becomes isotropic and is determined by small-scale stress anomalies due to irregularities in floe shape.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

The combined effects of porous asphalt surfacing and barriers on traffic noise

There is considerable interest in the use of porous asphalt (PA) surfacing on highways since physical and subjective assessments of noise have indicated a significant advantage over conventional non-porous surfaces such as hot rolled asphalt (HRA) used widely for motorway surfacing in the UK. However, it was not known whether the benefit of the PA surface was affected by the presence of roadside barriers. Noise predictions have been made using the Boundary Element Method (BEM) approach to determine the extent to which the noise reducing benefits of PA could be added to the screening effects of noise barriers in order to obtain the overall reduction in noise levels

Modelling the reorientation of sea-ice faults as the wind changes direction

A discrete-element model of sea ice is used to study how a 90° change in wind direction alters the pattern of faults generated through mechanical failure of the ice. The sea-ice domain is 400km in size and consists of polygonal floes obtained through a Voronoi tessellation. Initially the floes are frozen together through viscous–elastic joints that can break under sufficient compressive, tensile and shear deformation. A constant wind-stress gradient is applied until the initially frozen ice pack is broken into roughly diamond-shaped aggregates, with crack angles determined by wing-crack formation. Then partial refreezing of the cracks delineating the aggregates is modelled through reduction of their length by a particular fraction, the ice pack deformation is neglected and the wind stress is rotated by 90°. New cracks form, delineating aggregates with a different orientation. Our results show the new crack orientation depends on the refrozen fraction of the initial faults: as this fraction increases, the new cracks gradually rotate to the new wind direction, reaching 90° for fully refrozen faults. Such reorientation is determined by a competition between new cracks forming at a preferential angle determined by the wing-crack theory and at old cracks oriented at a less favourable angle but having higher stresses due to shorter contacts across the joints

A multithickness sea ice model accounting for sliding friction

A multithickness sea ice model explicitly accounting for the ridging and sliding friction contributions to sea ice stress is developed. Both ridging and sliding contributions depend on the deformation type through functions adopted from the Ukita and Moritz kinematic model of floe interaction. In contrast to most previous work, the ice strength of a uniform ice sheet of constant ice thickness is taken to be proportional to the ice thickness raised to the 3/2 power, as is revealed in discrete element simulations by Hopkins. The new multithickness sea ice model for sea ice stress has been implemented into the Los Alamos “CICE” sea ice model code and is shown to improve agreement between model predictions and observed spatial distribution of sea ice thickness in the Arctic.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Modeling and simulation of the anode in direct ethanol fuels cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this work, the objective is to characterize a mechanistic model for the anode of a direct ethanol fuel cell and perform appropriate simulations. The software Comsol Multiphysics (R) (and the Chemical Engineering Module) was used in this work. The software Comsol Multiphysics (R) is an interactive environment for modeling scientific and engineering applications using partial differential equations (PDEs). Based on the finite element method, it provides speed and accuracy for several applications. The mechanistic model developed here can supply details of the physical system, such as the concentration profiles of the components within the anode and the coverage of the adsorbed species on the electrode surface. Also, the anode overpotential-current relationship can be obtained. To validate the anode model presented in this paper, experimental data obtained with a single fuel cell operating with an ethanol solution at the anode were used. (C) 2008 Elsevier B.V. All rights reserved.

Movements and mechanical stresses in gas-filled flat plate solar collectors

Sealed gas filled flat plate solar collectors will have stresses in the material since volume and pressure varies in the gas when the temperature changes. Several geometries were analyzed and it could be seen that it is possible reducing the stresses and improve the safety factor of the weakest point in the construction by using larger area and/or reducing the distance between glass and absorber and/or change width and height relationship so the tubes are getting longer. Further it could be shown that the safety factor won't always get improved with reinforcements. It is so because when an already strong part of the collector gets reinforced it will expose weaker parts for higher stresses. The finite element method was used for finding out the stresses.

Minimization of stock weight during close-die forging of a spindle

In this paper, Finite Element method and full-scale experiments have been used to study a hot forging method for fabri-cation of a spindle using reduced initial stock size. The forging sequence is carried out in two stages. In the first stage, the hot rolled cylindrical billet is pre-formed and pierced in a closed die using a spherical nosed punch to within 20 mm of its base. This process of piercing or impact extrusion leads to high strains within the work piece but requires high press loads. In the second stage, the resulting cylinder is placed in a die with a flange chamber and upset forged to form a flange. The stock mass is optimized for complete die filling. Process parameters such as effective strain distribution, material flow and forging load in different stages of the process are analyzed. It is concluded from the simulations that minor modifications of piercing punch geometry to reduce contact between the punch and emerging vertical walls of the cylinder appreciably reduces the piercing load. In the flange chamber, a die surfaces angle of 52° instead of 45° is pro-posed to ensure effective material flow and exert sufficient tool pressure to achieve complete cavity filling. In order to achieve better compression, it is also proposed to shorten both the length of the inserted punch and the die “tongues” by a few mm.

Um estudo de percolação em barragens de terra, em regimes permanente e transiente, com a aplicação do método de elementos finitos

Este trabalho apresenta um estudo de fluxo de água em barragens de terra, em regimes permanente e transiente, com a utilização do Método de Elementos Finitos. No estudo de fluxo em regime permanente duas formas de abordar o problema são apresentadas e comparadas. A primeira considera, para a discretização da malha de elementos finitos, somente a região saturada, de maneira que a linha freática é obtida através de ajustes desta malha de elementos finitos. A segunda considera toda a região saturada-insaturada, sendo discretizado todo o domínio físico da barragem. A malha de elementos finitos não é modificada ao longo das iterações e a linha freática é obtida por interpolação dentro dos elementos, em função dos valores nodais do potencial de pressões. O desenvolvimento teórico das equações utilizadas para as duas formas de abardagem é apresentado, mostrando onde elas diferem entre si. No estudo de fluxo em regime transiente é utilizado apenas o esquema de malha fixa de elementos finitos.

Um modelo elasto-viscoplástico para análise de peças de concreto estrutural, submetidas a estados planos de tensão, através do método dos elementos finitos

O objetivo deste trabalho é desenvolver um modelo computacional, baseado no método dos elementos finitos, para o estudo de peças de concreto armado e protendido submetidas a estados planos de tensão. O estudo abrange situações de carga de curta e longa duração, onde consideram-se fluência e retração do concreto e relaxação do aço. São utilizados modelos constitutivos elasto-viscoplásticos para descrever o comportamento dos materiais. Implementou-se um modelo de camadas superpostas para melhor representar o comportamento do concreto, onde o material é composto de diversas camadas que sofrem a mesma deformação. Cada camada possui diferentes características materiais e a tensão total é obtida pela soma das diferentes contribuições de cada camada. Para a fissuração da concreto, utilizou-se um modelo de fissuras distribuídas, que leva em conta a contribuição do concreto entre fissuras. Tanto a amadura passiva como a de pratensão são introduzidas no modelo como uma linha de material mais rígido dentro do elemento de concreto. Os deslocamentos ao longo da armadura são referenciados aos deslocamentos nodais do elemento de concreto. Deste modo, obtém-se uma matriz de rigidez para a armadura com as mesmas dimensões que a matriz de rigidez do elemento de concreto, A matriz de rigidez do elemento concreto-aço é a soma das duas matrizes. Considera-se aderência perfeita entre o concreto e o aço. Os resultados obtidos com esse programa computacionai são comparados com valores experimentais disponíveis.