A structure-preserving geometric construction of a fully explicit discrete dynamical system equivalent to the Navier-Stokes equations based on conjugate Voronoi-Delaunay tessellations

The motion of viscous fluids is governed by the Navier-Stokes equations. The inherent nonlinearity of the Navier-Stokes equations has historically led to the widespread use of implicit global solvers or explicit schemes with artificial stabilization. In this work, we present a fully explicit computational framework based on a structure-preserving geometric formulation defined on a conjugate Voronoi-Delaunay tessellation. Unlike conventional approaches derived from differential operator discretization, the proposed approach constructs a discrete dynamical system directly from geometric coupling relations, in which the governing conservation laws emerge as exact algebraic conservation identities of the discrete structure.