Stabilization meshless method for convection-dominated problems |
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Authors: | Xiao-hua Zhang Jie Ouyang Jian-yu Wang |
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Affiliation: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China |
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Abstract: | It is well-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several tech- niques are proposed to overcome the instability issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal re- finement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all. |
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Keywords: | meshless method convection-diffusion problem stability method |
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