Periodic Navier Stokes Equations: PNS system within & external to embedded spheres of the 3-Torus: The mapping function at a 90 degree corner

TL;DR

This paper presents a solution for the third velocity component in the periodic Navier-Stokes equations at corners outside embedded spheres within a 3-torus lattice, addressing boundary behavior in complex geometries.

Contribution

It introduces a novel approach to solving the third velocity component at corners outside embedded spheres in the PNS system within a 3-torus.

Findings

Explicit solution for the third velocity component at corners outside spheres

Enhanced understanding of boundary conditions in PNS systems

Potential applications in fluid dynamics simulations involving complex geometries

Abstract

In this paper a solution for the third component of velocity for the Periodic Navier Stokes equations at the corners outside the sphere embedded in each cell of the lattice of $\mathbb{T}^3$ is presented.