Three-dimensional vortex methods

Technical Report · Wed Aug 01 04:00:00 EDT 1984

OSTI ID:6570179

Greengard, C A

Three-dimensional vortex methods for the computation of incompressible fluid flow are presented from a unified point of view. Reformulations of the filament method and of the method of Beale and Majda show them to be very similar algorithms; in both of them, the vorticity is evaluated by a discretization of the spatial derivative of the flow map. The fact that the filament method, the one which is most often used in practice, can be formulated as a version of the Beale and Majda algorithm in a curved coordinate system is used to give a convergence theorem for the filament method. The method of Anderson is also discussed, in which vorticity is evaluated by the exact differentiation of the approximate velocity field. It is shown that, in the inviscid version of this algorithm, each approximate vector of vorticity remains tangent to a material curve moving with the computed flow, with magnitude proportional to the stretching of this vortex line. This remains true even when time discretization is taken into account. It is explained that the expanding core vortex method converges to a system of equations different from the Navier-Stokes equations. Computations with the filament method of the inviscid interaction of two vortex rings are reported, both with single filaments in each ring and with a fully three-dimensional discretization of vorticity. The dependence on parameters is discussed, and convergence of the computed solutions is observed. 36 references, 4 figures.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6570179
• Report Number(s): LBL-18217; ON: DE85000391
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ALGORITHMS
COMPUTER CALCULATIONS
FLUID FLOW
INCOMPRESSIBLE FLOW
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
THREE-DIMENSIONAL CALCULATIONS
VORTEX FLOW