Vorticity-velocity formulation for three-dimensional steady compressible flows
- Yale Univ., New Haven, CT (United States)
The vorticity-velocity formulation of the Navier-Stokes equations is extended to the solution of three-dimensional compressible fluid flow and heat transfer problems. The basic governing equations are expressed in terms of three Poisson-like equations for the velocity components together with a vorticity transport equation and an energy equation. The resulting seven coupled partial differential equations are solved by a finite difference method on a single grid and a discrete solution is obtained by combining a steady-state and a time-dependent Newton's method. Once a converged solution is obtained, one of the velocity equations can be removed from the system and replaced by the continuity equation and a [open quotes]conservative[close quotes] solution is obtained by using the previous solution as a starting estimate for Newton's method with only a few additional iterations. The numerical procedure is evaluated by applying it to natural and mixed convection problems. The formulation is found to be stable at high Rayleigh numbers and it may be applied to a wide variety of flow and heat transfer problems.
- OSTI ID:
- 6629002
- Journal Information:
- Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 105:1; ISSN 0021-9991; ISSN JCTPAH
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420400* -- Engineering-- Heat Transfer & Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CALCULATION METHODS
COMPRESSIBLE FLOW
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
ENERGY TRANSFER
EQUATIONS
FINITE DIFFERENCE METHOD
FLUID FLOW
HEAT TRANSFER
ITERATIVE METHODS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
SIMULATION
THREE-DIMENSIONAL CALCULATIONS
VORTEX FLOW