A second-order projection method for the incompressible navier-stokes equations

doi:10.1016/0021-9991(89)90151-4

Journal of Computational Physics

Volume 85, Issue 2, December 1989, Pages 257-283

https://doi.org/10.1016/0021-9991(89)90151-4 Get rights and content

Abstract

In this paper we describe a second-order projection method for the time-dependent, incompressible Navier-Stokes equations. As in the original projection method developed by Chorin, we first solve diffusion-convection equations to predict intermediate velocities which are then projected onto the space of divergence-free vector fields. By introducing more coupling between the diffusion-convection step and the projection step we obtain a temporal discretization that is second-order accurate. Our treatment of the diffusion-convection step uses a specialized higher order Godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high Reynolds number. The Godunov procedure is second-order accurate for smooth flow and remains stable for discontinuous initial data, even in the zero-viscosity limit. We approximate the projection directly using a Galerkin procedure that uses a local basis for discretely divergence-free vector fields. Numerical results are presented validating the convergence properties of the method. We also apply the method to doubly periodic shear-layers to assess the performance of the method on more difficult applications.

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^∗: This work was performed, in part, under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. Partial support under Contract W-7405-Eng-48 was provided by the Applied Mathematical Sciences Program of the Office of Energy Research and by the Air Force Office of Scientific Research under Grant AFOSR-ISSA-870016.

^†: The work of this author was partially supported by the National Science Foundation under Grant DMS-87-3971.

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A second-order projection method for the incompressible navier-stokes equations

Abstract

J. Comput. Phys.

J. Comput. Phys.

J. Comput. Phys.

Mathematical Problems in the Dynamics of a Viscous Incompressible Flow

Arch. Rat. Mech. Anal.

Navier-Stokes Equations

Phys. Fluids

Int. J. Numer. Methods Fluids

Soviet Phys. Dokl.

Math. Comput.