• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권3호
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• pp.156-184
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• 2022

In this article, we propose a novel variational model for restoring color images corrupted by mixed multiplicative Gamma noise and additive Gaussian noise. The model involves a data-fidelity term that characterizes the mixed noise as an infimal convolution of two noise distributions and the saturation-value total variation (SVTV) regularization. The data-fidelity term facilitates suitable separation of the multiplicative Gamma and Gaussian noise components, promoting simultaneous elimination of the mixed noise. Furthermore, the SVTV regularization enables adequate denoising of homogeneous regions, while maintaining edges and details and diminishing the color artifacts induced by noise. To solve the proposed nonconvex model, we exploit an alternating minimization approach, and then the alternating direction method of multipliers is adopted for solving subproblems. This contributes to an efficient iterative algorithm. The experimental results demonstrate the superior performance of the proposed model compared to other existing or related models, with regard to visual inspection and image quality measurements.

• 한국해안·해양공학회논문집
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• 제31권4호
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• pp.229-239
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• 2019

산사태의 시간에 따른 전파를 모의하기 위해서 천수방정식을 사용하여 산사태 수치모형을 개발하였다. 하천 및 해양에서의 산사태에 모두 해석이 가능하도록 (b, s) 좌표로 표현된 천수방정식을 개발하였다. 산사태에서 발생하는 수치적인 불연속성을 극복하기 위해서 HLL approximate Riemann solver와 total variation diminishing (TVD) limiter를 사용한 유한체적법을 사용하였다. 댐파괴 흐름와 토석류의 각 경우에 수치해석을 수행한 결과를 해석해와 실험자료와 비교를 하였다. 그 결과 서로 유사함을 확인되었다. 본 모형을 사용하여 해상 산사태와 해저 산사태를 성공적으로 모의하였다. 해저 산사태에 비해 해상 산사태의 전파속도가 더 빠르고, 바닥경사가 급할수록 또는 거칠기가 작을수록 산사태 전파속도가 더 빨라짐을 확인하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제22권5호
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• pp.670-679
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• 1998

The solution of hyperbolic equation with wave nature has sharp discontinuties in the medium at the wave front. Difficulties encounted in the numrtical solution of such problem in clude among oth-ers numerical oscillation and the representation of sharp discontinuities with good resolution at the wave front. In this work inviscid Burgers equation and modified heat conduction equation is intro-duced as hyperboic equation. These equations are caculated by numerical methods(explicit method MacCormack method Total Variation Diminishing(TVD) method) along various Courant numbers and numerical solutions are compared with the exact analytic solution. For inviscid Burgers equa-tion TVD method remains stable and produces high resolution at sharp wave front but for modified heat Conduction equation MacCormack method is recommmanded as numerical technique.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권3호
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• pp.211-236
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• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.

• 천문학회보
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• 제39권1호
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• pp.57.2-57.2
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• 2014

Protostellar jets and outflows are signatures of star formation and promising mechanisms for driving supersonic turbulence in molecular clouds. We quantify outflow-driven turbulence through three-dimensional numerical simulations using an isothermal version of the total variation diminishing code. We drive turbulence in real space using a simplified spherical outflow model, analyze the data through density probability distribution functions (PDFs), and investigate density and velocity power spectra. The real-space turbulence-driving method produces a negatively skewed density PDF possessing an enhanced tail on the low-density side. It deviates from the log-normal distributions typically obtained from Fourier-space turbulence driving at low densities, but can provide a good fit at high densities, particularly in terms of mass-weighted rather than volume-weighted density PDF. We find shallow density power-spectra of -1.2. It is attributed to spherical shocks of outflows themselves or shocks formed by the interaction of outflows. The total velocity power-spectrum is found to be -2.0, representative of the shock dominated Burger's turbulence model. Our density weighted velocity power spectrum is measured as -1.6, slightly less that the Kolmogorov scaling values found in previous works.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• 한국해양공학회지
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• 제7권1호
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• pp.99-106
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• 1993

The use of Hermite cubic element, as a possible finite element computation of transport equations containing shocks, has been invesigated. In the present paper the hermite cubic elements are applied to both linear and nonlinear scalar one and two dimensional equations. In the one dimensional problems, numerical results by the hermite cubic element show better than those by the linear element, and the steady state solution by the hermite cubic element yields result with good resolution. This fact proves the superiority of the hermite cubic element in space differencing. In two dimensional case, the results by the hermite cubic element shows a boundary instability, and the use of higher order time differencing method may be necessary for fixing the problem.

• 한국수자원학회논문집
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• 제36권4호
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• pp.597-608
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• 2003

본 연구에서는 천수방정식을 이용하여 2차원 개수로에서 하상과 하폭이 급격히 변화하는 경우에 발생하는 천이류를 해석하였다. 불연속점 근처에서 발생하는 수치진동을 제어하면서 시간과 공간에 대한 2차 정확도를 확보하기 위하여 WAF 기법에 TVD 조건을 갖는 흐름률 제한자를 도입하였으며, Riemann해를 계산하기 위하여 3개의 전파속도를 고려하는 HLLC 방법을 이용하였다. 개수로에서 단면변화를 고려한 2차원 해석을 할 경우, 격자 구성과 경계 처리에서 어려움이 발생한다. 이와 같은 어려움을 해결하기 위하여 일반좌표계를 도입하여 하폭이 변화하는 구간에 발생하는 천이류를 수치모의하였다.

• 한국추진공학회지
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• 제1권1호
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• pp.46-54
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• 1997

본 연구에서는 공업적으로 널리 활용되고 있는 초음속 부족팽창 제트유동을 용이하게 예측하기 위하여, 종래의 수치계산 결과를 이용, 축대칭 및 2차원 초음속 부족팽창 제트유동에 대한 스케일링 식을 제안하였다. 본 연구에서 제안된 축대칭 및 2차원 제트유동에 관한 경험식들은 TVD수치계산 결과와 잘 일치하였으며, 노즐의 작동압력비가 주어지는 경우, 초음속 부족팽창 제트유동의 형태는 스케일링 식들에 의하여 잘 예측할 수 있었다.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 1997년도 제8회 학술강연회논문집
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• pp.75-84
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• 1997

Based upon the results of numerical calculation. empirical scaling equations were made for supersonic under-expanded jets in both axisymmetric and two dimensional flows. The objective of the present study is to obtain a straightforward method that can predict the under-expanded supersonic jets issuing from various kinds of nozzles. The present empirical equations were agreed with the calculation results of total variation diminishing difference scheme. The supersonic under-expanded jets operating with a given pressure ratio could be well predicted by the present scaling equations.