Finite-difference method for incompressible Navier-Stokes equations in arbitrary orthogonal curvilinear coordinates

  • Authors:

  • Nikolay Nikitin

  • Affiliations:

  • Institute of Mechanics of Moscow State University, Laboratory of General Aeromechanics, Moscow, Russian Federation

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

A finite-difference method for solving three-dimensional time-dependent incompressible Navier-Stokes equations in arbitrary curvilinear orthogonal coordinates is presented. The method is oriented on turbulent flow simulations and consists of a second-order central difference approximation in space and a third-order semi-implicit Runge-Kutta scheme for time advancement. Spatial discretization retains some important properties of the Navier-Stokes equations, including energy conservation by the nonlinear and pressure-gradient terms. Numerical tests cover Cartesian, cylindrical-polar, spherical, cylindrical elliptic and cylindrical bipolar coordinate systems. Both laminar and turbulent flows are considered demonstrating reasonable accuracy and stability of the method.