Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.     

A high-order discontinuous Galerkin method for wave propagation through coupled elastic–acoustic media

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic–acoustic media. A velocity–strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic–acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic–acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.     

Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.     

Microstructure and high-temperature corrosion behaviors of aluminide coatings by low-temperature pack aluminizing process

Aluminide coatings were produced on carbon steel and Fe-5Cr-Mo alloy at a relatively lower temperature below 600 °C in shorter treatment time by a combination of surface refinement process and pack aluminizing process. Repetitive ball impact, generated by mechanical vibration, caused the top-layer refinement of substrates in a conventional pack aluminizing process. The effects of temperature and treatment time on the formation of aluminide coatings were analyzed. The microstructure of the coatings was investigated by SEM, AFM and XRD. The aluminide coatings were one-layer, compacted structure with ultrafine grains and uniform elemental distribution. High-temperature oxidation and sulphidation tests were carried out at 600 °C in air for 200 h and 10% SO₂ + Ar gas mixture atmosphere for 50 h, respectively. The mass gains and spallation indicated that the aluminide coatings significantly improved the high-temperature oxidation and sulphidation resistance.     

Technically optimal inspection policy with arithmetical adaption

A process is considered whose quality deteriorates accordingto a constant failure intensity . As in practice it can be difficultto estimate the true value of the purpose of this paper isto present a strategy which can be applied without knowing .In order to maximize the number of conforming items per timeunit perfect inspections and renewals are performed. The lengthof the inspection interval is described by an arithmetical sequenceand changes by the time depending on perceived assignable causes.Optimal adaptive control plans provide nearly the same performanceas in the case when is known.     

Parallel globally adaptive quadrature on the KSR-1

New algorithms for parallel one-dimensional globally adaptive quadrature are developed. The algorithms are implemented on a Kendall Square Research KSR-1 parallel computer and numerical results are presented. The most successful algorithm gives significant speedups on a range of hard problems, including ones with singular integrands. Both authors acknowledge the support of the EEC Esprit Basic Research Action Programme, Project 6634 (APPARC). The second author acknowledges the support of the NATO Collaborative Research Grant 920037.     

DQAINF: an algorithm for automatic integration of infinite oscillating tails

We describe an automatic quadrature routine which is specifically designed for real functions having a certain type of infinite oscillating tails. The algorithm is designed to integrate a vector function over an infinite interval. A FORTRAN implementation of the algorithm is included.The algorithm combines an adaptive subdivision strategy with extrapolation and requires that the decay of all the functions in the vector is the same. The algorithm is based on the assumption that the oscillating behavior is due to a periodic function with the property that it changes sign when evaluated at points of distance half a period. We assume that this period is known. The algorithm offers a choice of three different quasi-linear extrapolation procedures, namely the Euler transformation and two modifications of this transformation.This work was supported by The Norwegian Research Council for Science and the Humanities.     

Microstructural evolution of AZ31 magnesium alloy subjected to sliding friction treatment

Microstructural evolution and grain refinement mechanism in AZ31 magnesium alloy subjected to sliding friction treatment were investigated by means of transmission electron microscopy. The process of grain refinement was found to involve the following stages: (I) coarse grains were divided into fine twin plates through mechanical twinning; then the twin plates were transformed to lamellae with the accumulation of residual dislocations at the twin boundaries; (II) the lamellae were separated into subgrains with increasing grain boundary misorientation and evolution of high angle boundaries into random boundaries by continuous dynamic recrystallisation (cDRX); (III) the formation of nanograins. The mechanisms for the final stage, the formation of nanograins, can be classified into three types: (i) cDRX; (ii) discontinuous dynamic recrystallisation (dDRX); (iii) a combined mechanism of prior shear-band and subsequent dDRX. Stored strain energy plays an important role in determining deformation mechanisms during plastic deformation.