Numerical solution methods using overset meshes have found wide use for decades, offering flexibility in handling complex geometries but requiring the process of domain assembly in order to achieve a valid mesh system. One aspect of this process is hole cutting, in which elements are selectively removed from the mesh to avoid intersection with solid bodies and excessive overlap, and which is accomplished through hole cutting methods such as direct cut and implicit hole cutting methods. Recent works by Liu et al. [1-3] introduced a new class of hole cutting methods, called elliptic hole cutting, that incorporate some aspects of both direct cut and implicit hole cutting methods and additionally use component-mesh-associated pseudo-temperature fields to aid the process. The fields are computed as finite element solutions to Poisson equations on each of the component meshes with source terms reflecting the relative mesh quality or priority of the component meshes. While improvements over implicit hole cutting methods were demonstrated, the elliptic hole cutting method still requires expensive mesh search operations. In this work, we propose new related methods, based on boundary element solution of Laplace's equation and radial basis function interpolation. Our approaches follow the basic idea of the elliptic hole cutting method but remove some of its limitations. In particular, our methods eliminate the use of the volume mesh in the computation of attachment fields, using only selected surface nodes, and avoids the necessity of a direct cut method to supply artificial boundary condition in the elliptic hole cutting method. We compare the relative merits of our proposed approaches and present an application to a multi-component airfoil geometry.
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