Generation of Volume Meshes by Extrusion from Surface Meshes of Arbitrary Topology

An algorithm to generate volume meshes by extrusion from surface meshes of arbitrary topology is presented. The algorithm utilizes a three-step, advancing layer scheme to extrude a smooth volume mesh starting from an initial surface mesh. First, a locally orthogonal reference mesh is algebraically generated for the layer. The reference mesh is then smoothed using a locally three-dimensional Poisson-type mesh generation equation that is generalized to smooth extruded meshes of arbitrary surface topology. By using the Poisson equation, control functions developed for elliptic grid generation may be employed to improve mesh quality. The Poisson smoother is modified in concave regions to enhance the robustness of the advancing layer scheme. Several preliminary examples are included to demonstrate the efficacy of the approach.