An upwind nodal integral method for incompressible fluid flow

Journal Article · Sat May 01 04:00:00 EDT 1993 · Nuclear Science and Engineering; (United States)

OSTI ID:6521038

Esser, P D ^[1]; Witt, R J ^[2]

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1. Studsvik of America, Inc., Idaho Falls, ID (United States)
2. Univ. of Wisconsin, Madison, WI (United States)

An upwind nodal solution method is developed for the steady, two-dimensional flow of an incompressible fluid. The formulation is based on the nodal integral method, which uses transverse integrations, analytical solutions of the one-dimensional averaged equations, and node-averaged uniqueness constraints to derive the discretized nodal equations. The derivation introduces an exponential upwind bias by retaining the streamwise convection term in the homogeneous part of the transverse-integrated convection-diffusion equation. The method is adapted to the stream function-vorticity form of the Navier-Stokes equations, which are solved over a nonstaggered nodal mesh. A special nodal scheme is used for the Poisson stream function equation to properly account for the exponentially varying vorticity source. Rigorous expressions for the velocity components and the no-slip vorticity boundary condition are derived from the stream function formulation. The method is validated with several benchmark problems. An idealized purely convective flow of a scalar step function indicates that the nodal approximation errors are primarily dispersive, not dissipative, in nature. Results for idealized and actual recirculating driven-cavity flows reveal a significant reduction in false diffusion compared with conventional finite difference techniques.

• OSTI ID: 6521038
• Journal Information: Nuclear Science and Engineering; (United States), Journal Name: Nuclear Science and Engineering; (United States) Vol. 114:1; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400 -- Engineering-- Heat Transfer & Fluid Flow
665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
CALCULATION METHODS
CONVECTION
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
FINITE DIFFERENCE METHOD
FLUID FLOW
HEAT TRANSFER
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
MASS TRANSFER
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
STEADY FLOW
TESTING
VALIDATION