Generation of smooth grids with line control for scattering from multiple obstacles

A new approach to generate structured grids for two-dimensional multiply connected regions with several holes is proposed. The bounding curves may include corners or cusps. The new algorithm constitutes an extension of the Branch Cut Grid Line Control (BCGC) technique introduced byVillamizar et al. [V. Villamizar, O. Rojas, J. Mabey, Generation of curvilinear coordinates on multiply connected regions with boundary-singularities, J. Comput. Phys. 223 (2007) 571–588] to domains with a finite number of holes. Regions with multiple holes are reduced to several contiguous single hole subregions. Then, the BCGC algorithm is applied to each single hole subregion producing a smooth grid with line control. Finally, the subregions with their respective grids are joined and their interfaces are smoothed resulting a globally smooth grid. The advantages of the novel grids are revealed by employing them to numerically solve acoustic scattering problems in the presence of multiple complexly shaped obstacles.