Hexahedral mesh smoothing using a direct method

Abstract

This paper develops a generalisation of the mesh smoothing direct method proposed by Balendran, to three dimensions by applying its methodology to smoothed hexahedral meshes. A geometric criteria is used where irregular quadrilaterals are converted to regular quadrilaterals on each face of the hexahedron using a local stiffness matrix. This matrix is then converted to a spatial stiffness matrix with reference to absolute coordinates in order to assemble the geometrical stiffness matrix as a global stiffness matrix. The fixing of boundary conditions is analysed and results obtained in a series of hexahedral meshes, used in finite difference method analysis, are illustrated. To evaluate the quality of the obtained results, a degree of uniformity is calculated and a comparative study of the improvement obtained in each zone of the hexahedral mesh is conducted. The proposed method permits the marking out of the portions of mesh in which a Laplacian smoothening fails to improve the mesh quality, therefore, requiring the use of other methods in which inserted mesh points are taken into account.