B-spline Methods in Fluid Dynamics

Abstract

Basis splines (B-splines) are basis functions for piecewise polynomials having a high level of derivative continuity. They possess attractive properties for complex flow simulations: they have compact support, provide a straightforward handling of boundary conditions and grid nonuniformities, yield numerical schemes with high resolving power, and the order of accuracy is a mere input parameter. This paper reviews progress made in the development and application of B-spline numerical methods to computational fluid dynamics. Basic approximation properties of B-spline schemes are discussed, and their relationship with conventional numerical methods is reviewed. Some fundamental developments towards spline methods in complex geometries are covered. These include local interpolation methods, fast solution algorithms on Cartesian grids, block-structured discretization and compatible pressure bases for the Navier-Stokes equations. Finally, application of some of these techniques to the computation of viscous incompressible flows is presented.