In this dissertation, a novel method to extrude near-body meshes from surface meshes of arbitrary topology that exploits topologically adaptive generalized elements to improve mesh quality is presented. Specifically, an advancing layer algorithm to generate near-body meshes which are appropriate for viscous fluid flows is discussed. First, an orthogonal two-layer algebraic reference mesh is generated. 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. Local quality improvement operations such as edge collapse, face refinement, and local reconnection are performed in each layer to drive the mesh toward isotropy. An automatic marching thickness reduction algorithm is used to extrude from multiple geometries in close proximity. A global face refinement algorithm is used to improve the transition from the extruded mesh to the voidilling tetrahedral mesh. A few example meshes along with quality plots are presented to demonstrate the efficacy of the algorithms developed.