Multidomain, Sparse, Spectral-tau Method for Helically Symmetric Flow

We consider the application of a multidomain, sparse, and modal spectral-tau method to the helically reduced Navier Stokes equations describing pipe flow. This work (i) formulates the corresponding modal approximations, (ii) describes improved boundary conditions for the helically reduced equations, and (iii) constructs iterative solutions of the corresponding elliptic problem that arises in the reduction. Regarding (iii), we also present and test a method for preconditioning the matching conditions between subdomains, a method based on statistical sampling and the interpolative decomposition. Although the following application is only discussed in our concluding section, a partial motivation for this work has been our ongoing development of similar spectral methods for the construction binary neutron star spacetimes.