New approach for solving stationary nonlinear Navier-Stokes equations in non-convex domain

TL;DR

This paper introduces a numerical method for solving stationary nonlinear Navier-Stokes equations in polygonal domains with reentrant corners, achieving first-order convergence regardless of corner angle.

Contribution

The method provides a novel approach that guarantees first-order convergence in non-convex domains with reentrant corners, overcoming previous limitations related to corner angles.

Findings

Achieves first-order convergence in non-convex domains

Works for domains with reentrant corners greater than π

Applicable to rotation and convective forms of Navier-Stokes equations

Abstract

In the paper, an approach for the numerical solution of stationary nonlinear Navier-Stokes equations in rotation and convective forms in a polygonal domain containing one reentrant corner on its boundary, that is, a corner greater than ${\pi}$ is considered. The method allows us to obtain the 1st order of convergence of the approximate solution to the exact one with respect to the grid step h, regardless of the reentrant corner value.