ADAPTIVE TRIANGULATION OF EVOLVING, CLOSED, OR OPEN SURFACES BY THE ADVANCING-FRONT METHOD

The advancing-front method is adapted to describe the evolution of ope n or closed three-dimensional surfaces in terms of an unstructured gri d consisting of quadratic triangular elements. In science and engineer ing applications, the surface may be identified with a material interf ace, a free boundary, or a moving front. In the numerical method, the geometrical properties of the surface and the coordinates of the trian gle vertices are computed either in terms of available analytical expr essions, or by means of interpolation through an underlying coarse gri d. The shape and size of the curved triangular elements are determined by the maximum magnitude of the mean or directional local surface cur vature. Two algorithms are implemented: the first one for simply conne cted open surfaces bounded by closed lines, and for closed surface wit h plane symmetry; and the second for closed surfaces. In the case of o pen surfaces, the discretization front advances from a one-dimensional boundary grid that traces the bounding curve. The boundary grid is ge nerated either by a one-dimensional version of the advancing-front met hod, or by requiring a set Of criteria based on local line representat ion with circular area. In the case of closed surfaces, the discretiza tion front emanates from the point of the maximum mean curvature. In b oth cases, the algorithm also interpolates to generate the values of s urface geometrical or physical variables such as temperature or concen tration of a surface-active agent. The method was tested by following the motion of several passive and active surfaces evolving under the a ction of specified fields of flow, while performing occasional regridd ing to ensure adequate spatial resolution. In one test, the large defo rmation of a viscous drop subjected to an infinite simple shear flow a t vanishing Reynolds number was computed into the regime where a cigar -like shape is established, thereby extending previous numerical compu tations for small and moderate deformations and reproducing experiment ally observed shapes. Overall, the adaptive-front method emerges as an important tool in numerical studies of free boundaries or moving fron ts and should be useful in a broad range of applications. (C) 1998 Aca demic Press.