An example of the Rvachev function method

Abstract

We present a Rvachev function method with the Chebysev collocation for the stability analysis of fluid flow. The strategy is to construct an approximate solution that satisfies all boundary conditions exactly. As an example, we consider the stability problem of the two-dimensional flow of an incompressible viscous liquid near a circular cylinder. The results coincide well with the reference data. The method is simpler than the widely used spectral/hp element method, in particular because it does not require mesh generation, and the collocation algorithm does not handle the boundary conditions or any geometric information.