CMES-Vol. 93, No. 5, 2013

Open Access

ARTICLE

Thermocapillary Motion of a Spherical Drop in a Spherical Cavity
Tai C. Lee¹, Huan J. Keh²
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 317-333, 2013, DOI:10.3970/cmes.2013.093.317
Abstract A theoretical study of the thermocapillary migration of a fluid sphere located at an arbitrary position inside a spherical cavity is presented in the quasisteady limit of small Reynolds and Marangoni numbers. The applied temperature gradient is perpendicular to the line through the drop and cavity centers. The general solutions to the energy and momentum equations governing the system are constructed from the superposition of their fundamental solutions in the spherical coordinates originating from the two centers, and the boundary conditions are satisfied by a multipole collocation method. Results for the thermocapillary migration velocity of… More >

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ARTICLE

Accuracy of Quarter-point Element in Modeling Crack-tip Fields
G. P. Nikishkov¹
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 335-361, 2013, DOI:10.3970/cmes.2013.093.335
Abstract Accuracy of the quarter-point and transition elements is investigated on one- and two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the stress intensity factor is studied. Solution accuracy can be improved using special distribution of element sizes and increasing the element integration order in the radial direction. More >

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Three-dimensional Fluid Flow Simulations Using GPU-based Particle Method
K. Kakuda¹, T. Nagashima¹, Y. Hayashi¹, S. Obara¹, J. Toyotani¹, S. Miura², N. Katsurada³, S. Higuchi³, S. Matsuda³
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 363-376, 2013, DOI:10.3970/cmes.2013.093.363
Abstract The application of a GPU-based particle method to three-dimensional incompressible viscous fluid flow problems is presented. The particle approach is based on the MPS (Moving Particle Semi-implicit) scheme using logarithmic weighting function to stabilize the spurious oscillatory solutions for solving the Poisson equation with respect to the pressure fields by using GPU-based SCG (Scaled Conjugate Gradient) method. Numerical results demonstrate the workability and the validity of the present approach through the dam-breaking flow problem and flow behavior in a liquid ring pump with rotating impeller blades. More >

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A Simple Proper Orthogonal Decomposition Method for von Karman Plate undergoing Supersonic Flow
Dan Xie¹, Min Xu²
CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 377-409, 2013, DOI:10.3970/cmes.2013.093.377
Abstract We apply a simple proper orthogonal decomposition (POD) method to compute the nonlinear oscillations of a degenerate two-dimensional fluttering plate undergoing supersonic flow. First, the von Karman’s large deflection theory and quasi-steady aerodynamic theory are employed in constructing the governing equations of the simply supported plate. Then, the governing equations are solved by both the Galerkin method and the POD method. The Galerkin method is accurate but sometimes computationally expensive, since the number of degrees of freedom (dofs) required is relatively large provided that nonlinearity is strong. The POD method can be used to capture… More >

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