A staggered grid, high-order accurate method for the incompressible Navier-Stokes equations

  • Authors:

  • Nikolaos A. Kampanis;John A. Ekaterinaris

  • Affiliations:

  • Foundation for Research and Technology-Hellas, Institute of Applied and Computational Mathematics, Heraklion, Crete, Greece;Foundation for Research and Technology-Hellas, Institute of Applied and Computational Mathematics, Heraklion, Crete, Greece and School of Mechanical and Aerospace Engineering, University of Patras ...

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

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Abstract

A high-order accurate, finite-difference method for the numerical solution of the incompressible Navier-Stokes equations is presented. Fourth-order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite-difference formulas. High-order accuracy in time is obtained by marching the solution with Runge-Kutta methods. The incompressibility constraint is enforced for each Runge-Kutta stage iteratively either by local pressure correction or by a Poisson-equation based global pressure correction method. Local pressure correction is carried out on cell by cell basis using a local, fourth-order accurate discrete analog of the continuity equation. The global pressure correction is based on the numerical solution of a Poisson-type equation which is discretized to fourth-order accuracy, and solved using GMRES. In both cases, the updated pressure is used to recompute the velocities in order to satisfy the incompressibility constraint to fourth-order accuracy. The accuracy and efficiency of the proposed method is demonstrated in test problems.