The Physical Influence Scheme applied to staggered unstructured grids for solving fluid flow problems

Abstract

In this article, a finite volume formulation for solving the Navier-Stokes equations using unstructured hybrid grids and a staggered arrangement of variable pressure and velocity is presented. In this manner, a tight spatial pressure-velocity coupling is ensured without compromising geometrical flexibility. A second contribution of this work lays upon proposing a suitable interpolation function for the convected velocities in the momentum equations. For this purpose, we employ the so-called “Physical Influence Scheme (PIS),” which fully incorporates all physical phenomena involved, namely convection, diffusion, and pressure effects. Each term corresponding to each physical phenomenon is carefully addressed. We present numerical experiments that show the suitability of the PIS for the staggered finite volume formulation and highlight the importance of including diffusion and pressure effects (in addition to convection) into the interpolation function.

Disclosure statement

The authors declare that they have no conflict of interests.

This research has been independently conducted by the authors with no external funding resources.