• Journal of computational fluids engineering
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• v.3 no.1
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

• Journal of the Korean Society for Marine Environment & Energy
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• v.2 no.2
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• pp.70-77
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• 1999

The disturbance of oil-water interface confined between tandem fences caused by a sequence of traveling vortices below the interface is investigated. The traveling vortices are assumed to be those detached from the tip of the fore fence. The potential flow is assumed and the density interface is replaced as a sheet of vortex. The shape of the interface is predicted by tracing a finite number of marker particles placed at the interface. The velocity of the marker particles is determined by the Biot-Savart integral along the vortex sheet plus the contribution from the traveling point vortices. The rate of change of vortex-sheet strength is predicted by using an evolution equation for vorticity. The calculated results obtained for various conditions demonstrate that the large amplitude of interfacial wave following the moving vortek can be generated by the vortices.

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.7
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• pp.769-778
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• 2005

The velocity and pressure fields of a ship's Weis-Fogh type propulsion mechanism are studied in this paper using an advanced vortex method. The wing (NACA0010 airfoil) and channel are approximated by source and vortex panels. and free vortices are introduced away from the body surfaces. The viscous diffusion of fluid is represented using the core-spreading model to the discrete vortices. The velocity is calculated on the basis of the generalized Biot-Savart law and the pressure field is calculated from an integral, based on the instantaneous velocity and vorticity distributions in the flow field. Two-dimensional unsteady viscous flow calculations of this propulsion mechanism are shown. and the calculated results agree qualitatively with the measured thrust and drag due to un-modeled large fluctuations in the measured data.

• Journal of KSNVE
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• v.7 no.2
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• pp.215-222
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• 1997

The flow and acoustic fields due to a vortex ring interaction with a rigid sphere are simulated numerically. The flow field is regarded as three-dimensional inviscid and incompressible. The vorticity is assumed to be concentrated inside the finite core of vortex filament. The vortex filament curve, described by parabolic blending curve function, is used to effectively solve the modified Biot-Savart equation. The interaction between a vortex ring and a rigid sphere using the parabolic blending curve is calculated. The trajectory of the vortex ring is obtained with several different initial positions between the ring and the sphere. The force variations acting on the sphere are calculated by using the boundary integral method. Finally, we can also obtain the acoustic signals at the far field observation positions from the force variations acting on the rigid surface. We can find that the dipole axis of the directivity patterns are rotated during the interacting phenomena.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.47-52
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• 2002

We present an improved Lagrangian vortex method in 2-D incompressible unsteady viscous flows, which is based on a mesh-free integral approach of the velocity-vorticity formulation. Vorticity fields are represented by discrete vortex blobs that are updated by the Lagrangian vorticity transport with the particle strength exchange scheme. Velocity fields are expressed in a form of the Helmholtz decomposition, which are calculated by a fast algorithm of the Biot-Savart integration with a smoothed kernel and by a well-established panel method. No-slip condition is enforced through viscous diffusion of vorticity from a solid body into field. The vorticity flux is determined in such a way that spurious slip velocity vanishes. Through the comparison with the existing finite volume scheme for the transient vortical flows around an impulsively started cylinder at Reynolds number Re=550, we would obtain a more accurate scheme for vortex methods in complicated flows.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.5
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• pp.733-743
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• 2000

We solve the integral representation of the Navier-Stokes equations in a lagrangian view by tracking the particles, which have vortex strengths. We simulate the unsteady viscous flow around an impulsively started cylinder using the vortex particle method. Particles are advanced via the Biot-Savart law for a lagrangian evolution of particles. The particle strength is modified based on the scheme of particle strength exchange. The solid boundary satisfies the no-slip boundary condition by the vorticity generation algorithm. We newly modify the diffusion scheme and the boundary condition for simulating an unsteady flow efficiently. To save the computation time, we propose the mixed scheme of particle strength exchange and core expansion. We also use a lot of panels to ignore the curvature of the cylinder, and not to solve the evaluation of the surface density. Results are compared to those from other theoretical and experimental works.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.1-10
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• 1998

This paper presents a vorticity-based numerical method for analyzing an incompressible Newtonian viscous flow around an impulsively started cylinder. The Navier-Stockes equations have a natural Helmholtz decomposition. The vorticity transport equation and the pressure equation are derived from this decoupled form. The associated boundary conditions are dynamic for the vorticity and pressure variables representing the coupling relation between them and the force balance on the wall. The various numerical treatments for solving the governing equations are introduced. According to Wu et al.(1994), the boundary conditions are decoupled, keeping the dynamic relation between vorticity and pressure. The vorticity transport equation is formulated by FVM and TVD(Total Variation Diminishing) scheme is used for the convection term. An integral approach similar to the panel method is used to obtain the velocity field for a given vorticity field and the pressure field, instead of the conventional differential approaches. In the numerical process, the structured grid is generated. The results are compared to existing numerical and analytic results for the validity of the present method.