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Regularized directional do-nothing boundary conditions for the Navier-Stokes equations: Analytical and numerical study

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  • Nogueira, Pedro
  • Silvestre, Ana L.

Abstract

We consider the steady 2D and 3D Navier-Stokes equations with homogeneous mixed boundary conditions and the action of an external force. The classical do-nothing (CDN) boundary condition is replaced by a regularized directional do-nothing (RDDN) condition which depends on a parameter 0<δ≪1. After establishing the well-posedness of the Navier-Stokes equations with RDDN condition, we prove the convergence, as δ→0, to the solution of the Navier-Stokes equations with directional do-nothing (DDN) condition. The use of the RDDN condition in comparison with the CDN and DDN conditions is illustrated with 2D numerical simulations. The theoretical convergence result as δ→0 is also confirmed by our numerical results.

Suggested Citation

  • Nogueira, Pedro & Silvestre, Ana L., 2025. "Regularized directional do-nothing boundary conditions for the Navier-Stokes equations: Analytical and numerical study," Applied Mathematics and Computation, Elsevier, vol. 499(C).
    • Handle: RePEc:eee:apmaco:v:499:y:2025:i:c:s0096300325001250
    DOI: 10.1016/j.amc.2025.129398
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