• 호남수학학술지
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• 제41권2호
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• 한국분무공학회지
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• 제1권1호
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• pp.44-54
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• 1996

A theoretical and experimental study was carried out on the prediction of drop size distribution of the pressure swirl atomizer. Drop size distribution was obtained by using maximum entropy formal ism. Several constraints in the form of the definition of mean diameter were used in this formulation in order to avoid the difficulties of the estimating source terms. In this study $D_{10}$ was only introduced into the formulation as a constraint. A drop size obtained by using linear Kelvin-Helmholtz instability theory was considered as an unknown characteristic length scale. As a result, the calculated drop size was agreed well with measured mean diameter, particularly with $D_{32}$. The predicted drop size distribution was agreed welt with experimental data measured wi th Malvern 2600.

• 소음진동
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• 제7권6호
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• pp.975-984
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• 1997

A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

• Wind and Structures
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• 제13권4호
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• pp.363-374
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• 2010

Appropriate scaling methods for wind tunnel modelling of building internal pressures induced through a dominant opening were investigated. In particular, model cavity volume distortion and geometric scaling of the opening details were studied. It was found that while model volume distortion may be used to scale down buildings for wind tunnel studies on internal pressure, the implementation of the added volume must be done with care so as not to create two cavity resonance systems. Incorrect scaling of opening details was also found to generate incorrect internal pressure characteristics. Furthermore, the effective air slug or jet was found to be longer when the opening was near a floor or sidewall as evidenced by somewhat lower Helmholtz frequencies. It is also shown that tangential flow excitation of Helmholtz resonance for off-centre openings in normal flow is also possible.

• 한국분무공학회지
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• 제2권1호
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• pp.8-17
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• 1997

A study has been carried out on the instability of a conical liquid sheet by using the linear instability theory. Various analytical methods using the Kelvin-Helmholtz instability theory were tried to examine the wave growth on cylindrical liquid sheets. Cylinderical liquid sheets were extended to the case with the conical sheets. Perturbations due to tangential motion as well as longitudinal one were taken into account. And it was assumed the the breakup occurs when amplitude ratio exceeds exp(12), drop sizes were predicted only by theoretical approach. The predicted drop size agreed well with the measured Sauter mean diameter, $D_{32}$.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2008년도 춘계학술대회논문집
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• pp.280-285
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• 2008

The helmholtz resonator with the perforated neck has demerits that the absorption performance is not so outstanding in an anti-resonance frequency and high frequency bandwidth. In order to overcome these problems, in the paper, a resonator combined with porous material is proposed. The absorption performances of resonators are measured by two-microphone method and estimated by transfer matrix method. The experimentally measured values of normal absorption coefficients agree well with the corresponding values from the transfer matrix method. Because of the porous material, it is shown that the absorption performance have been significantly improved in the anti-resonance frequency and high frequency bandwidth.

• 대한전기학회논문지
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• 제37권8호
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• pp.521-527
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• 1988

At present superconducting magnets have been feasible for many applications which require high field or highly homogeneous field that it is too difficult to be produced by conventional electromagnets. This paper is a stuny on Donble Helmholtz superconducting magnet and newly configurated superconducting magnet that realize highly homogeneous field with the minimum magnet volume. Nonlinear programming method is effectively used for the minimum volume of superconducting magnet that realizes the desired field intensity and high homogeneity. The results on Double Helmholtz and newly configurated superducting magnets that are presented in this paper are largely improved.

• 대한기계학회논문집
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• 제18권4호
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• pp.1081-1086
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• 1994

The phenomena called "combustion instabilities" in a solid-propellant rocket motor may be viewed as sustaining or amplifying pressure waves. Energy is supplied by combustion processes near the surface of the burning propellant. T-burner method is used to determine the response function of the propellant to the pressure wave. But initial tests were failed because of the Helmholtz resonation inside the T-burner. Acoustic analysis of the original T-burner is carried out and suppression techniques for the Helmholtz oscillation are introduced.ntroduced.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.101-113
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• 2018

The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권4호
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.