Steady Incremental Viscosity Splitting Method for solving the stationary Navier-Stokes equation
Numerical Analysis
2026-05-07 v1 Numerical Analysis
Abstract
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each nonlinear iteration, the scheme requires solving an elliptic PDE for the velocity variable and a system with an SPD matrix for the pressure variable, which remains the same across all nonlinear iterations. The method can also be interpreted as an algebraic splitting approach. We prove boundedness and geometric convergence. Numerical tests illustrate the efficiency of the proposed algorithm.
Keywords
Cite
@article{arxiv.2605.04778,
title = {Steady Incremental Viscosity Splitting Method for solving the stationary Navier-Stokes equation},
author = {Aziz Takhirov and Driss Yakoubi},
journal= {arXiv preprint arXiv:2605.04778},
year = {2026}
}