A numerical layer resolving method for the flow over a curved surface

We investigate the model problem of flow of a viscous incompressible fluid past a symmetric curved surface when the stream is parallel to its axis. When the Reynolds number is large, this problem is known to exhibit boundary layers which grow downstream and eventually shows a “3-D character” because of the large curvature of the body in the transverse direction. This problem does not have solutions in closed form. We employ a direct layer resolving numerical method that provides solutions that are accurate and robust. To show the direct numerical method is a robust layer-resolving method for the sphere, we provide extensive experimental evidence. We show that all results obtained, such as velocity components and their scaled derivatives, are robust with respect to the viscosity.