Jin Li^1,2, De-hao Yu^3,4

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 103-126, 2014, DOI:10.3970/cmes.2014.102.103

Abstract The generalized composite middle rectangle rule for the computation of Hilbert integral is discussed. The pointwise superconvergence phenomenon is presented, i.e., when the singular point coincides with some a priori known point, the convergence rate of the rectangle rule is higher than what is global possible. We proved that the superconvergence rate of the composite middle rectangle rule occurs at certain local coordinate of each subinterval and the corresponding superconvergence error estimate is obtained. By choosing the superconvergence point as the collocation points, a collocation scheme for solving the relevant Hilbert integral equation is presented and an error estimate is… More >

T. Ghisu¹, B. Arca², G. Pellizzaro², P. Duce²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.1, pp. 83-102, 2014, DOI:10.3970/cmes.2014.102.083

Abstract Level-set approaches are efficient and versatile methods for solving interface tracking problems and have been used in recent years to describe wildland fire propagation. Being based on an Eulerian description of the spread problem, their numerical implementation offers improved computational agility and better portability to parallel computing environments with respect to vector-based simulators. The use of a continuous representation of the fire perimeter in place of the binary formulation used in Cellular Automata avoids the commonly observed distortion of the fire shape. This work presents an algorithm for fire-spread simulation based on a level-set formulation. The results are compared to… More >

Weiwei Zhang¹, Yufeng Nie¹, Li Cai¹, Nan Qi²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.1, pp. 55-82, 2014, DOI:10.3970/cmes.2014.102.055

Abstract In this paper, we derive an adaptive mesh generation method for discretizing the incompressible flow using node-based local grids. The flow problem is described by the Stokes equations which are solved by a stabilized low-order P1-P1 (linear velocity, linear pressure) mixed finite element method. The proposed node-based adaptive mesh generation method consists of four components: mesh size modification, a node placement procedure, a node-based local mesh generation strategy and an error estimation technique, which are combined so as to guarantee obtaining a conforming refined/coarsened mesh. The nodes are considered as particles with interaction forces, which are generated by dynamic simulation… More >

G Devaraj¹, Shashi Narayan¹, Debasish Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.1, pp. 1-54, 2014, DOI:10.3970/cmes.2014.102.001

Abstract This work sets forth a 'hybrid' discretization scheme utilizing bivariate simplex splines as kernels in a polynomial reproducing scheme constructed over a conventional Finite Element Method (FEM)-like domain discretization based on Delaunay triangulation. Careful construction of the simplex spline knotset ensures the success of the polynomial reproduction procedure at all points in the domain of interest, a significant advancement over its precursor, the DMS-FEM. The shape functions in the proposed method inherit the global continuity (C^p-1) and local supports of the simplex splines of degree p. In the proposed scheme, the triangles comprising the domain discretization also serve as background… More >

D. Ishihara¹, T. Horie¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 421-440, 2014, DOI:10.3970/cmes.2014.101.421

Abstract In this study, a projection method for the monolithic interaction system of an incompressible fluid and a structure using a new algebraic splitting is proposed. The proposed method splits the monolithic equation system into the equilibrium equations and the pressure Poisson equation (PPE) algebraically using the intermediate velocity in the nonlinear iterations. Since the proposed equilibrium equation satisfies the interface condition, the proposed method is strongly coupled. Moreover, the proposed PPE enforces the incompressibility constraint. Different from previous studies, the proposed algebraic splitting never generates any Schur complement. The proposed method is applied to a channel with a flexible flap,… More >

N.A. Dumont ¹, D. Huamán¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 387-419, 2014, DOI:10.3970/cmes.2014.101.387

Abstract The present paper starts with Mindlin’s theory of the strain gradient elasticity, based on three additional constants for homogeneous materials (besides the Lamé’s constants), to arrive at a proposition made by Aifantis with just one additional parameter. Aifantis’characteristic material length g², as it multiplies the Laplacian of the Cauchy stresses, may be seen as a penalty parameter to enforce interelement displacement gradient compatibility also in the case of a material in which the microstructure peculiarities are in principle not too relevant, but where high stress gradients occur. It is shown that the hybrid finite element formulation – as proposed by… More >

Csaba Gáspár¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 365-386, 2014, DOI:10.3970/cmes.2014.101.365

Abstract The Method of Fundamental Solutions (MFS) is investigated for 3D potential problem in the case when the source points are located along the boundary of the domain of the original problem and coincide with the collocation points. This generates singularities at the boundary collocation points, which are eliminated in different ways. The (weak) singularities due to the singularity of the fundamental solution at the origin are eliminated by using approximate but continuous fundamental solution instead of the original one (regularization). The (stronger) singularities due to the singularity of the normal derivatives of the fundamental solution are eliminated by solving special… More >

Zhengzheng Cao¹, Yuejin Zhou^1,2, Ping Xu¹, Jiawei Li¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 351-364, 2014, DOI:10.3970/cmes.2014.101.351

Abstract In accordance with the influence of underground mining on the deformation and failure of a shallow-buried gas pipeline, the pipe-soil interaction during mining is classified into two stages, namely coordinated deformation stage and partial hanging stage. According to the mechanical characteristics of the buried pipeline in each stage, the models of a) a beam on an elastic foundation, b) an elastic beam under uniform load, and c) a vertical and horizontal bending beam are introduced in a mining subsidence zone to mechanically analyze, respectively a) the pipeline in non-mining subsidence zone, b) the pipeline at the coordinated deformation stage, and… More >

Po-Wei Li¹, Chia-Ming Fan^1,2, Chun-Yu Chen¹, Cheng-Yu Ku¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 319-350, 2014, DOI:10.3970/cmes.2014.101.319

Abstract A combination of the generalized finite difference method (GFDM), the implicit Euler method and the Newton-Raphson method is proposed to efficiently and accurately analyze the density-driven groundwater flows. In groundwater hydraulics, the problems of density-driven groundwater flows are usually difficult to be solved, since the mathematical descriptions are a system of time- and space-dependent nonlinear partial differential equations. In the proposed numerical scheme, the GFDM and the implicit Euler method were adopted for spatial and temporal discretizations of governing equations. The GFDM is a newly-developed meshless method and is truly free from time-consuming mesh generation and numerical quadrature. Based on… More >

Christina Babenko¹, Roman Chapko², B. Tomas Johansson³

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.5, pp. 299-317, 2014, DOI:10.3970/cmes.2014.101.299

Abstract We consider the numerical solution of the Laplace equations in planar bounded domains with corners for two types of boundary conditions. The first one is the mixed boundary value problem (Dirichlet-Neumann), which is reduced, via a single-layer potential ansatz, to a system of well-posed boundary integral equations. The second one is the Cauchy problem having Dirichlet and Neumann data given on a part of the boundary of the solution domain. This problem is similarly transformed into a system of ill-posed boundary integral equations. For both systems, to numerically solve them, a mesh grading transformation is employed together with trigonometric quadrature… More >