CMES-Vol. 35, No. 2, 2008

Open Access

ARTICLE

A Highly Accurate MCTM for Inverse Cauchy Problems of Laplace Equation in Arbitrary Plane Domains
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 91-112, 2008, DOI:10.3970/cmes.2008.035.091
Abstract We consider the inverse Cauchy problems for Laplace equation in simply and doubly connected plane domains by recoverning the unknown boundary value on an inaccessible part of a noncircular contour from overspecified data. A modified Trefftz method is used directly to solve those problems with a simple collocation technique to determine unknown coefficients, which is named a modified collocation Trefftz method (MCTM). Because the condition number is small for the MCTM, we can apply it to numerically solve the inverse Cauchy problems without needing of an extra regularization, as that used in the solutions of direct problems for Laplace equation.… More >

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ARTICLE

Solutions for Incompressible Viscous Flow in a Triangular Cavity using Cartesian Grid Method
B. M. Pasquim¹, V. C. Mariani²
CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 113-132, 2008, DOI:10.3970/cmes.2008.035.113
Abstract This study presents a Cartesian grid method and its application to solve a steady flow in a lid-driven triangular two-dimensional cavity. The evolution of stream function and vorticity inside a triangular lid-driven cavity, when the Reynolds number changes from 1 to 6000, is presented. For space discretization on the interior of triangular cavity orthogonal Cartesian grid is used. Then, using this grid, trapezoidal volumes appear in the interface between solid and fluid. For a suitable treatment of these volumes the Eulerian-Lagrangian methodology is used. The Navier-Stokes equations are solved numerically using finite-volume method. On the basis of the numerical studies… More >

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Application of Meshless Local Petrov-Galerkin (MLPG) Method in Cloth Simulation
Weiran Yuan^1,2, Yujun Chen^2,3, André Gagalowicz², Kaixin Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 133-156, 2008, DOI:10.3970/cmes.2008.035.133
Abstract In this paper we present an approach to cloth simulation which models the deformation based on continuum mechanics and discretized with Meshless Local Petrov-Galerkin (MLPG) Method. MLPG method, which involves not only a meshless interpolation for trial functions, but also a meshless integration of the local weak form, has been considered as a general basis for the other meshless methods. By this way, the mechanical behavior of cloth is consistent and united, which is independent of the resolutions. At the same time, point sampled models, which neither have to store nor to maintain globally consistent topological information, are available for… More >

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A Lie-Group Shooting Method Estimating Nonlinear Restoring Forces in Mechanical Systems
Chein-Shan Liu ¹
CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.2, pp. 157-180, 2008, DOI:10.3970/cmes.2008.035.157
Abstract For an inverse vibration problem of nonlinear mechanical system to estimate displacement- and velocity-dependent restoring force, we transform the equation of motion into a parabolic type partial differential equation (PDE). Then by a semi-discretization of the PDE, the inverse vibration problem is formulated as a multi-dimensional two-point boundary value problem with unknown sources, allowing a closed-form estimation through a Lie-group shooting method to construct the restoring force surface over phase plane. Only one set of displacements measured at sampling time points is used in the estimation. The new method does not require to assume a priori the functional form of… More >

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