Physical Sciences and Mathematics Commons^™

A High-Order Radial Basis Function (Rbf) Leray Projection Method For The Solution Of The Incompressible Unsteady Stokes Equations, Edward J. Fuselier, Varun Shankar, Grady B. Wright

Mathematics Faculty Publications and Presentations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs …