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Abstract <p> The fully conservative finite volume discretization of the incompressible Navier–Stokesequations in cylindrical coordinates is constructed on a staggered grid. The proposeddiscretization ensures momentum conservation in the computational domain and massconservation within the control volumes for pressure and velocity components. The energyconservation equation directly follows from the discrete momentum equation. Both conservativeand nonconservative forms of convective terms are approximated. The proposed discretecounterpart of the vector Laplace operator is self-adjoint and negative definite.</p>

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A Fully Conservative Finite-Difference Scheme for Three-Dimensional Navier–Stokes Equations in Cylindrical Coordinates

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • A. O. Gusev,
  • O. S. Mazhorova

摘要

Abstract

The fully conservative finite volume discretization of the incompressible Navier–Stokesequations in cylindrical coordinates is constructed on a staggered grid. The proposeddiscretization ensures momentum conservation in the computational domain and massconservation within the control volumes for pressure and velocity components. The energyconservation equation directly follows from the discrete momentum equation. Both conservativeand nonconservative forms of convective terms are approximated. The proposed discretecounterpart of the vector Laplace operator is self-adjoint and negative definite.