Stokes Flow around a Hypersphere in n-Dimensional Space and Its Visualization

Abstract

We derived the Stokes equations and velocity potential around a hyperspherical obstacle in n-dimensional space. The objectives of this study were to understand the hyperspace through the physics in the space and to bring the analytical solution of fluid flow in hyperspace for numerical simulation. The equations were obtained from the n-dimensional Navier-Stokes equation assuming the low Reynolds number flow. These were generalized formulae from a 3-dimensional system to an n-dimensional one. Our results show that the effect of the hyperspherical obstacle on the uniform flow is localized in higher dimensional spaces. We visualized the flow using the collections of hypersections.