• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.667-677
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• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.

• Structural Engineering and Mechanics
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• 제14권1호
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• pp.71-84
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• 2002

A finite element formulation for the time-domain analysis of linear transient elastodynamic problems is presented based on the weak form obtained by applying the Galerkin's method to the integro-differential equations which contain the initial conditions implicitly and does not include the inertia terms. The weak form is extended temporally under the assumptions of the constant and linear time variations of field variables, since the time-stepping algorithms such as the Newmark method and the Wilson ${\theta}$-method are not necessary, obtaining two kinds of implicit finite element equations which are tested for numerical accuracy and convergency. Three classical examples having finite and infinite domains are solved and numerical results are compared with the other analytical and numerical solutions to show the versatility and accuracy of the presented formulation.

• 한국전산유체공학회지
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• 제3권1호
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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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• 한국전산유체공학회 1998년도 춘계 학술대회논문집
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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.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 추계 학술대회논문집
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• pp.37-42
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• 2003

A vorticity-velocity integro-differential formulation of incompressible Wavier-Stokes equations is described, focusing on a scheme for calculating pressure fields in application of the Lagrangian vortex method in connection with panel methods. It deals with the dynamic coupling among velocity, vorticity and pressure, and the Helmholtz decomposition of the velocity field, through a comparative study with the Eulerian finite volume method, we provide an extensive understanding of the Lagrangian vortex methods for numerical simulations of viscous flows around arbitrary bodies.

• 대한조선학회논문집
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• 제40권2호
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• pp.21-27
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• 2003

The phenomena of vortex shedding around a cylinder oscillating harmonically in a fluid at rest are investigated by a two-dimensional numerical simulation of the Navier-Stokes equations. The simulation is based on a vorticity-velocity integro-differential formulation dealing with vorticity, velocity and pressure variables. Three combinations of Reynolds number(Re) and Keulegan-Carpenter number(KC) were taken to investigate the associated vortex development around the cylinder in the different flow regimes. Drag and lift forces are computed to describe their dominant frequency modulation which is related to the vortex shedding and to the harmonic motion of the cylinder.