A second-order projection method for the incompressible Navier--Stokes equations

Journal Article · Thu Nov 30 23:00:00 EST 1989 · Journal of Computational Physics; (USA)

DOI:https://doi.org/10.1016/0021-9991(89)90151-4· OSTI ID:6990503

Bell, J B; Colella, P ^[1]; Glaz, H M ^[2]

---

1. Lawrence Livermore National Laboratory, Livermore, California 94550 (USA)
2. University of Maryland College Park, Maryland 20742 (USA)

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 convegence 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. {copyright} 1989 Academic Press, Inc.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6990503
• Journal Information: Journal of Computational Physics; (USA), Journal Name: Journal of Computational Physics; (USA) Vol. 85:2; ISSN 0021-9991; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
CONVECTION
DIFFERENTIAL EQUATIONS
DIFFUSION
DIRICHLET PROBLEM
ENERGY TRANSFER
EQUATIONS
HEAT TRANSFER
LAYERS
MASS TRANSFER
MATHEMATICAL LOGIC
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS