CMES-Vol. 101, No. 5, 2014

Open Access

ARTICLE

On the Numerical Solution of the Laplace Equation with Complete and Incomplete Cauchy Data Using Integral Equations
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 >

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Generalized Finite Difference Method for Numerical Solutions of Density-driven Groundwater Flows
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 >

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Mechanical Response Analysis and Safety Assessment of Shallow-Buried Pipeline under the Influence of Mining
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 >

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