Galerkin Approximations to Flows within Slabs, Spheres, and Cylinders

This Letter introduces infinite-order accurate and efficiently implementable Galerkin (spectral) approximations to time-dependent incompressible flows within slabs, spheres, and cylinders with either rigid no-slip or free-slip boundaries. The unusual choice of Chebyshev polynomials as Galerkin expansion functions is crucial for the efficiency of the method.