A second-order projection method for viscous, incompressible flow

Conference · Wed Apr 01 04:00:00 EST 1987

OSTI ID:6855581

Bell, J B; Colella, P; Glaz, H M

In this paper we describe a second-order projection method for the time-dependent, incompressible Navier Stokes equations. The numerical method consists of three separate parts: a time-stepping strategy that ensures second-order accuracy, a numerical approximation of the Hodge projection, and a second-order discretization of the nonlinear convection terms. The basic requirements for second-order temporal accuracy are discussed in a semi-discrete form. Approximation of the projection using a discrete Galerkin formulation based on determination of a local basis for discretely divergence free vector fields is described. A specialized, second-order Godunov procedure is developed for discretization of the nonlinear convective terms. The Godunov method remains stable and non-oscillatory as Reynolds number tends to infinity. From a linear algebraic point of view the overall algorithm requires only the solution of symmetric, positive-definite systems that are ideally suited to iterative methods. Numerical results are presented validating the convergence properties of the method.

• Research Organization: Lawrence Livermore National Lab., CA (USA); Maryland Univ., College Park (USA). Dept. of Mathematics
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6855581
• Report Number(s): UCRL-96428; CONF-8706104-1; ON: DE87008209
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUID FLOW
INCOMPRESSIBLE FLOW
NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS