Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems

ZHANG Xiao-hua; DENG Ji-heng

doi:10.3879/j.issn.1000-0887.2014.11.008

Volume 35 Issue 11

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ZHANG Xiao-hua, DENG Ji-heng. Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1249-1258. doi: 10.3879/j.issn.1000-0887.2014.11.008

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Research on the Meshless Solving Algorithm for 3D Steady ConvectionDiffusion Problems

doi: 10.3879/j.issn.1000-0887.2014.11.008

College of Science, China Three Gorges University, Yichang, Hubei 443002, P.R.China

Funds: The National Natural Science Foundation of China(11102101；11171181)

Received Date: 2014-06-07
Rev Recd Date: 2014-10-15
Publish Date: 2014-11-18

Abstract

Abstract

The meshless method is a numerical algorithm for the simulation of flow fields in complicated shapes and solves fluid mechanics problems without grids. In order to improve the computation efficiency of meshless methods based on the Galekrin weak integration form for solving 3D steady convection-diffusion problems, a meshless shape function was proposed based on convex-polyhedral nodal influence domain in the discrete space. Then with a properly selected factor of nodal influence radius, the node-searching process was avoided and the bandwidth of the stiffness matrix for the system was reduced. With a factor of nodal influence radius at 1.01 during the calculation, the shape function of the meshless method almost possesses interpolation properties and the imposition of essential boundary conditions is simplified as that for the FEM. The numerical results of 2 exemplary steady convection-diffusion problems for 3D cubic regions show that: compared with the traditional meshless methods, the present meshless method based on convex-polyhedral nodal influence domain enables the computing time to be reduced by up to 42% without impairing the calculation accuracy. Finally, in the cases that both the computation efficiency and the accuracy are highly demanded, this meshless method based on convex-polyhedral nodal influence domain is suggested for the solution of 3D steady convection-diffusion problems.
- meshless method,
- 3D steady convection-diffusion,
- computation efficiency,
- convex-polyhedral nodal influence domain

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References(11)

References

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