Steady Incremental Viscosity Splitting Method for solving the stationary Navier-Stokes equation
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| Format: | Preprint |
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2026
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| _version_ | 1866914534566920192 |
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| author | Takhirov, Aziz Yakoubi, Driss |
| author_facet | Takhirov, Aziz Yakoubi, Driss |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Steady Incremental Viscosity Splitting Method for solving the stationary Navier-Stokes equation Takhirov, Aziz Yakoubi, Driss Numerical Analysis 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. |
| title | Steady Incremental Viscosity Splitting Method for solving the stationary Navier-Stokes equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.04778 |