• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.133-142
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• 2000

We consider some numerical solution methods for equilibrium equations Af + E$^{T}$ λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible fluid flow. We also suggests some iterative methods based upon substructuring scheme..

• Journal of the Chungcheong Mathematical Society
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• v.5 no.1
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• pp.151-157
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• 1992

The objective of this paper is to study two dimensional waves on the interface between two immiscible, invicid and incompressible fluid bounded by two rigid varing boundaries when gravity and surface tension appear. By using unfied asymptotic method, a K-dV equation with higher order terms from which many model equations for the fluid domain can be obtained, is derived.

• Journal of Mechanical Science and Technology
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• v.17 no.3
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• pp.457-466
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• 2003

In this paper, the numerical finite element formulations were derived for the linearized Navier-Stokes' equations with assumptions of two-dimensional incompressible, homogeneous viscous fluid field, and small oscillation and the FAMD (Fluid Added Mass and Damping) code was developed for practical applications calculating the fluid added mass and damping. In formulations, a fluid domain is discretized with C$\^$0/-type quadratic quadrilateral elements containing eight nodes using a mixed interpolation method, i.e., the interpolation function for the velocity variable is approximated by a quadratic function based on all eight nodal points and the interpolation function for the pressure variable is approximated by a linear function based on the four nodal points at vertices. Using the developed code, the various characteristics of the fluid added mass and damping are investigated for the concentric cylindrical shell and the actual hexagon arrays of the liquid metal reactor cores.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.216-221
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• 2004

In two dimensional incompressible flaws, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint and hence achieve an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flaw analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flaw showed the present procedure to be stable, very efficient and useful in flaw analyses in conjunction with hierarchical elements.

• Journal of Ocean Engineering and Technology
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• v.17 no.5 s.54
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• pp.11-18
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• 2003

In two-dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure (HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint hence, achieving an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared (CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper and efficient iterative procedure for higher order finite element formulation has not been available, thus far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient, and useful in flow analyses, in conjunction with hierarchical elements.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.83-90
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• 2004

Substructuring methods are usually used in finite element structural analyses. In this study a multi-level substructuring algorithm is developed and proposed as a possible candidate for incompressible fluid solves. Finite element formulation for incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et.al.[5]. The present algorithm consists of four stages such as a gathering stage, a condensing stage, a solving stage and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At highest level, each subdomain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each subdomain has been replaced by a sequential static condensation. The global algebraic system arising feom the assembly of each subdomains is solved using Conjugate Gradient Squared(CGS) method. In this case, pre-conditioning techniques usually accompanied by iterative solvers are not needed.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.91-98
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• 2004

In two dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a stabilized finite element formulation. The stabilization has been peformed by a modified residual method proposed by Illinca et. al.[3]. The stabilization which is necessary to escape from the LBB constraint renders an equal order formulation. In this paper, we increased the order of interpolation whithin an element up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.289-294
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• 2010

Numerical stud of an oscillating body in incompressible fluid is performed. Stabilized finite element method comprising of Streamline-Upwind/Petrov-Galerkin (SUPG) and Pressure-Stabilizing/Petrov-Galerkin (PSPG) formulations of linear triangular elements was employed to solve 2D incompressible Navier-Stokes equations whereas the motion of the body was considered by incorporating the arbitrary Langrangian-Eulerian(ALE) formulation. An algebraic moving mesh strategy is utilized for obtaining body conforming mesh deformation at each time step. Two tests cases, namely motion of a circular cylinder and of an airfoil in incompressible flow were analyzed. The model is first validated against the stationary cases and then the capability to handle moving boundaries is demonstrated.

• Ocean Systems Engineering
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• v.1 no.3
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• pp.207-222
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• 2011

A stabilized incompressible smoothed particles hydrodynamics (ISPH) method is utilized to simulate free falling rigid body into water domain. Both of rigid body and fluid domain are modeled by SPH formulation. The proposed source term in the pressure Poisson equation contains two terms; divergence of velocity and density invariance. The density invariance term is multiplied by a relaxed parameter for stabilization. In addition, large eddy simulation with Smagorinsky model has been introduced to include the eddy viscosity effect. The improved method is applied to simulate both of free falling vessels with different materials and water entry-exit of horizontal circular cylinder. The applicability and efficiency of improved method is tested by the comparisons with reference experimental results.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.67-82
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• 2006

In this paper, we present a finite difference method for the implementation of the rotation of a circular cylinder in the incompressible flow field by solving the two-dimensional unsteady Navier-Stokes equations. The approach is to use staggered grid method so that the accuracy and order of convergence of the associated algorithms can be maintained. The proposed method is easy to be implemented and is effective. A set of simulations for the flow dynamics is provided to show the computational results.