Generalized Stokes eigenfunctions: A new trial basis for the solution of incompressible Navier-Stokes equations (Q1339527)

A new algorithm is proposed to simulate turbulence in a realistic range of Reynolds number and geometry. The basis functions are constructed as the eigenfunctions of a multidimensional Sturm-Liouville problem, called the singular Stokes eigensystem. The Galerkin projections reduce to a system of ordinary differential equations where the techniques for the analysis of dynamical systems are also useful. Three computational domains: channel flow, grooved channel flow, and eddy-promoter flow are considered, and the boundary conditions are mixed Dirichlet and periodic conditions. The solutions are obtained for a wide range of Reynolds number.