Abstract：The type of badly shaped elements in tetrahedral mesh was summarized. The estimating criterion of the types of different badly shaped elements was proposed through the numerical calculation. With the criterion, the types, distributions and causes of the badly shaped elements in centrifugal pumps were analyzed，an error function was put forward and taken as the object function of the optimal algorithmbased smoothing by researching available functions of tetrahedral element quality and considering the edge mass restriction. The minimum of the error function could be obtained by using BFGS(broyden fletcher goldfarb shanno) method to smooth tetrahedral mesh． Finally, the improved optimizationbased smoothing, Laplacian smoothing and swapping technique were integrated to optimize the poorquality mesh elements generated by advancing front technique(AFT) method and Delaunay triangulation method．The practical application of the optimization algorithm for a centrifugal pump shows that the worst mesh elements can be eliminated and the whole mesh quality can be improved obviously．So the algorithm can be used well in tetrahedral mesh optimization of centrifugal pumps.
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