The least-squares meshfree method for the steady incompressible viscous flow

Authors:
Xiang Kun Zhang;Kie-Chan Kwon;Sung-Kie Youn
Affiliations:
Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Gusung-dong,Yusung-ku, Taejon 305-701, Republic of Korea;Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Gusung-dong,Yusung-ku, Taejon 305-701, Republic of Korea;Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Gusung-dong,Yusung-ku, Taejon 305-701, Republic of Korea
Venue:
Journal of Computational Physics
Year:
2005

Citing 4
Cited 1

Least-square finite elements for Stokes problem

Computer Methods in Applied Mechanics and Engineering
Smoothing and accelerated computations in the element free Galerkin method

Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
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Computational geometry: algorithms and applications
Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method

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Original article: Development of a meshless Galerkin boundary node method for viscous fluid flows

Mathematics and Computers in Simulation

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Abstract

A least-squares meshfree method (LSMFM) based on the first-order velocity-pressure-vorticity formulation for two-dimensional steady incompressible viscous flow is presented. The discretization of all governing equations is implemented by the least-squares method. The equal-order moving least-squares (MLS) approximation is employed. Gauss quadrature is used in the background cells constructed by the quadtree algorithm and the boundary conditions are enforced by the penalty method. The matrix-free element-by-element Jacobi preconditioned conjugate method is applied to solve the discretized linear systems. A numerical example with analytical solution for the Stokes problem is devised to analyze the error estimates of the LSMFM. Also, cavity-driven flow for the Stokes problem and the flow past a circular cylinder at low Reynolds numbers for the steady incompressible viscous flow are solved. Through the comparisons of the LSMFM's results with other experimental and numerical results, the numerical features of the presented LSMFM are investigated and discussed.