• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.7
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• pp.586-591
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• 2007

The effects of cancellation errors on the convergence characteristics of preconditioned Euler equations at low Mach numbers are analyzed. Flows in a two-dimensional channel with a circular bump are calculated at different Mach numbers. It is shown that the cancellation error in the energy equation grows faster than those in the other equations as the Mach number decreases. It is also shown that the cancellation problem of the energy equation can be alleviated by multiplying the inversion of the preconditioner.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.186-191
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• 1999

An Euler solver is developed to predict accurate aerodynamic data such as lift coefficient, drag coefficient, and moment coefficient. The conservation law form of the compressible Euler equations are used in the generalized curvilinear coordinates system. The Euler solver uses a finite volume method and the second order Roe's flux difference splitting scheme with min-mod flux limiter to calculate the fluxes accurately. An implicit scheme which includes the boundary conditions is implemented to accelerate the convergence rate. The multi-block grid is integrated into the flow solver for complex geometry. The flowfields are analyzed around NACA 0012 airfoil in the cases of $M_{\infty}=0.75,\;\alpha=2.0\;and\;M_{\infty}=0.80,\;\alpha=1.25$. The numerical results are compared with other numerical results from the literature. The final goal of this research is to prepare a robust and an efficient Navier-Stokes solver eventually.

• Journal of the Korean Society of Propulsion Engineers
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• v.8 no.1
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• pp.27-37
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• 2004

The convergence characteristics of preconditioned Euler equations were studied. A perturbation analysis was conducted to understand the behavior of the preconditioned Euler equations. Various speed flows in a two-dimensional channel with a 10％ circular arc in the middle of the channel were calculated. Roe's FDS scheme was used for spatial discretization and the LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of pressure and velocity were maintained regardless of the Mach numbers but that the convergence characteristics of temperature were strongly related to the Mach number and became worse as the Mach number decreased. The perturbation analysis well explained the trend of the convergence characteristics and showed that the convergence characteristics are strongly related with the behavior o( the Preconditioning matrix.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.127-136
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• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.693-701
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• 2000

In this paper, we investigate a generalization of the Ulam stability problem of the 3-dimensional Euler-Lagrange functional equation f(x-y-z)+f(x)+f( y)+f(z)= f(x-y) +f(y+z) +f(z-x)

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.607-619
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• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.175-177
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• 2003

The convergence characteristics of the LV scheme for the Euler equations have been investigated by using the Von Neumann stability analysis. The results indicated that the convergence rate is governed by a specific combination of CFD parameters. Based on this insight, it is shown that the convergence characteristics of the LV scheme is not deteriorated at any grid aspect-ratio as long as the local time step is defined based on the parameter combination. The numerical results demonstrated that this time step definition provide a uniform convergence for grid aspect-ratios between one to$1{\times}10^{4}$.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.51 no.10
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• pp.560-567
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• 2002

This paper presents the calculation of opening characteristics for puffer GCB with the equations of the flow field and the motion of the driving mechanism. To obtain the stroke curve, the motion equation is solved simultaneously with the Euler equations. For a given Piston location, the flow field is solved. The pressure inside the Puffer chamber is then used to calculate the moving velocity and the new position of the piston. The FVFLIC method is employed to solve the axisymmetric Euler equations and the motion equation is solved by the Runge-Kutta method. The method is applied to the puffer GCB model and the stroke curve and the pressure rise in puffer chamber under no load condition are compared with the measured ones.

• Advances in nano research
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• v.12 no.2
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• pp.139-150
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• 2022

This paper presents sets of explicit analytical equations that compute the static displacements of nanobeams by adopting the nonlocal elasticity theory of Eringen within the framework of Euler Bernoulli and Timoshenko beam theories. Castigliano's theorem is applied to an equivalent Virtual Local Beam (VLB) made up of linear elastic material to compute the displacements. The first derivative of the complementary energy of the VLB with respect to a virtual point load provides displacements. The displacements of the VLB are assumed equal to those of the nonlocal beam if nonlocal effects are superposed as additional stress resultants on the VLB. The illustrative equations of displacements are relevant to a few types of loadings combined with a few common boundary conditions. Several equations of displacements, thus derived, matched precisely in similar cases with the equations obtained by other analytical methods found in the literature. Furthermore, magnitudes of maximum displacements are also in excellent agreement with those computed by other numerical methods. These validated the superposition of nonlocal effects on the VLB and the accuracy of the derived equations.

• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.78-84
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• 2001

A dual-time stepping algorithm combined with a parallelized multigrid DADI method is presented to predict the dynamic damping coefficients. The Basic Finner model is chosen to validate the prediction capability of the present unsteady Euler method. The linearity of the pitch- and roll-damping coefficients is shown in the low angular rates and the interesting large drop and stiff increment in transonic region for roll-damping coefficients are explained in detail. Through the analysis for the pressure distributions at Mach number 1.0 to 1.2, the sudden drop results from the normal shock and the stiff increment of roll-damping reflects the transition of the normal shock to the oblique shock. The results also show that the Euler equations can give the damping coefficients with a comparable accuracy.