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  • Meshless Local Petrov-Galerkin Simulation of Buoyancy-Driven Fluid Flow and Heat Transfer in a Cavity with Wavy Side Walls
  • Abstract As some new applications of the meshless local Petrov-Galerkin method (MLPG) with unity as the test function, a number of buoyancy-driven fluid flow natural convection heat transfer problems in cavities with differentially-heated wavy side walls were analyzed. Cavities with a single wavy wall on one side as well as two wavy walls erected on both sides were considered. For the cases of the double wavy walls, two different configurations in terms of the two walls facing each other on the two sides of the cavities symmetrically or non-symmetrically were investigated. All the simulations performed in this work were based on…
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  • Thin Film Flow Over and Around Surface Topography: a General Solver for the Long-Wave Approximation and Related Equations
  • Abstract The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptive time stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the same form as the base…
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  • On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion
  • Abstract We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical…
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  • Topological Derivative-Based Optimization of Micro-Structures Considering Different Multi-Scale Models
  • Abstract A recently proposed algorithm for micro-structural optimization, based on the concept of topological derivative and a level-set domain representation, is applied to the synthesis of elastic and heat conducting bi-material micro-structures. The macroscopic properties are estimated by means of a family of multi-scale constitutive theories where the macroscopic strain and stress tensors (temperature gradient and heat flux vector in the heat conducting case) are defined as volume averages of their microscopic counterparts over a Representative Volume Element (RVE). Several finite element-based examples of micro-structural optimization are presented. Three multi-scale models, providing an upper and a lower bound for the macroscopic…
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  • Particle Methods for a 1D Elastic Model Problem: Error Analysis and Development of a Second-Order Accurate Formulation
  • Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative of given functions, as well…
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  • Geometry-related Treatments for Three-dimensional Meshless Method
  • Abstract The meshless method has a distinct advantage over other methods in that it requires only nodes without an element mesh which usually induces time-consuming work and inaccuracy when the elements are distorted during the analysis process. However, the element mesh can provide more geometry information for numerical simulation, without the need to judge if the nodes or quadrature points are inside the analysis domain which happens in the meshless method, since the analysis domain is defined by the element's edges or faces and the quadrature points are all inside the elements. Because the analysis model with only nodes for the…
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  • Dispersion of One Dimensional Stochastic Waves in Continuous Random Media
  • Abstract Second, or higher, order harmonics have great potential in fatigue life prediction. In this study, the dispersion properties of waves propagating in the nonlinear random media are investigated. An one dimensional nonlinear model based on the nonlinear Hikata stress-strain relation is used. We applied perturbation method, the Liouville transformation and the smoothing approximation method to solve the one dimensional nonlinear stochastic wave equation. We show easily that the dispersion equations for all higher order terms will be the same with the corresponding linear random medium by perturbation method. The linear stochastic equation with two random coefficients is greatly simplified to…
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  • A 3D Numerical Model for a Flexible Fiber Motion in Compressible Swirling Airflow
  • Abstract A numerical method is developed for modeling the dynamics of a flexible fiber immersed in a compressible swirling flow. The modeling approach is based on combining an Eulerian finite volume formulation for the fluid flow and a Lagrangian small-deformation formulation for the dynamics of the fiber. The fiber is modeled as a chain of beads connected through mass-less rods. The bending and twisting deformation of the fiber are represented by the displacements of the successive beads. A computational strategy is proposed for the computation of the fluid parameters at the center of discrete fiber sections. To deal with the fiber-wall…
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  • Dynamic Analysis of Porous Media Considering Unequal Phase Discretization by Meshless Local Petrov-Galerkin Formulations
  • Abstract In this work, meshless methods based on the local Petrov-Galerkin approach are employed for the time-domain dynamic analysis of porous media. For the spatial discretization of the pore-dynamic model, MLPG formulations adopting Gaussian weight functions as test functions are considered, as well as the moving least square method is used to approximate the incognita fields. For time discretization, the generalized Newmark method is adopted. The present work is based on the u-p formulation and the incognita fields of the coupled analysis in focus are the solid skeleton displacements and the interstitial fluid pore pressures. Independent spatial discretization is considered for…
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