Solenoidal bases for numerical studies of transition in pipe flow

Abstract

In this paper, solenoidal basis functions are employed in numerical studies of transition in incompressible pipe flow. The bases are formulated in terms of Legendre polynomials, which are more favorable both for the functional form of the basis functions and for the inner product integrals arising in the Galerkin projection scheme. The projection is performed onto the dual solenoidal basis set to eliminate the pressure gradient term from the governing equations. This simplifies the numerical approach to the problem and the resulting scheme is used to study the nonlinear stability of pipe flow. Some preliminary results are compared with those found in the literature.