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A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation

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  • Bonaventura, Luca
  • Ferretti, Roberto
  • Rocchi, Lorenzo

Abstract

A numerical method for the two-dimensional, incompressible Navier–Stokes equations in vorticity-streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the reconstruction of the streamfunction. A description of the discretization of Dirichlet boundary conditions for the semi-Lagrangian approach to diffusion terms is also presented. Numerical experiments on classical benchmarks for incompressible flow in simple geometries validate the proposed method.

Suggested Citation

  • Bonaventura, Luca & Ferretti, Roberto & Rocchi, Lorenzo, 2018. "A fully semi-Lagrangian discretization for the 2D incompressible Navier–Stokes equations in the vorticity-streamfunction formulation," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 132-144.
    • Handle: RePEc:eee:apmaco:v:323:y:2018:i:c:p:132-144
    DOI: 10.1016/j.amc.2017.11.030
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    References listed on IDEAS

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    1. Belopolskaya, Ya. & Milstein, G. N., 2003. "An approximation method for Navier-Stokes equations based on probabilistic approach," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 201-211, August.
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    Cited by:

    1. Li, Xiaoli & Rui, Hongxing, 2019. "Stability and convergence of characteristic MAC scheme and post-processing for the Oseen equations on non-uniform grids," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 94-111.

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