• Water Engineering Research
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• v.4 no.4
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• pp.175-185
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• 2003

A numerical model to analyze dam break flows has been developed based on approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using finite volume method and the numerical flux are reconstructed with weighted averaged flux (WAF) method. The developed model is verified. The first verification problem is about idealized dam break flow on wet and dry beds. The second problem is about experimental data of dam break flow. From the results of the verifications, very good agreements have been observed

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.205-205
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• 2022

본 연구에서는 심해 선형파 조건에서 수중 투과성 방파제 주변의 유속장에 대해 nonhomogeneous Riemann-Hilbert problem을 이용한 해석해 및 수치해를 도출하고, 이를 반사계수와 투과계수를 산정하는 데에 활용한다. 여러 개의 얇은 투과성 판이 일렬로 배열되어 수중에 고정되어있고 규칙파가 작용하는 경우, Riemann-Hilbert problem을 정의할 수 있다. 본 연구에서는 얇은 판으로 이루어진 수중 방파제에 대한 homogeneous Riemann-Hilbert problem을 푸는 것을 넘어, 투과성 판으로 이루어진 수중 방파제에 대해 nonhomogeneous Riemann-Hilbert problem을 정의하고, 이에 대해 무한경계조건과 판 근처에서의 유속장 경계조건을 이용해 해석해를 유도하였다. 투과성 방파제의 경우 permeable boundary를 가지므로 제시한 상황은 기하학적 비선형성을 지닌다. 이에 대해 투수성을 기초로 미소 매개변수를 정의하고, 섭동법(perturbation method)을 이용해 유속장에 대한 leading order solution과 first order solution을 도출하였다. Leading order solution은 Evans (1970) 등의 선행연구에서 제시한 해와의 비교를 통해 그 타당성을 검증하였고, First order solution을 이용해 반사계수와 투과계수를 산정하여 방파제의 투수성이 유속장에 미치는 영향을 고려하였다. 아울러 수치해를 도출하여 해석해의 결과와 비교 및 분석하였다. 본 연구에서 제시한 해석해는 방파제에 가해지는 힘을 산정하는 등 다양한 방향으로 활용 가능하며, 향후 수치해나 실험값을 비교, 검증하기 위한 기초 자료로써 활용될 수 있다.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.743-765
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• 2019

Conceptual and procedural knowledge of integration is necessary not only in calculus but also in real analysis, complex analysis, and differential geometry. However, students show not only focused understanding of procedural knowledge but also limited understanding on conceptual knowledge of integration. So they are good at computation but don't recognize link between several concepts. In particular, Riemann sum is helpful in solving applied problem, but students are poor at understanding structure of Riemann sum. In this study, we try to investigate understanding on conceptual and procedural knowledge of integration and to analyze errors. Conducting experimental class of Riemann sum, we investigate the understanding of Riemann sum structure and so present the implications about improvement of integration teaching.

• East Asian mathematical journal
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• v.27 no.1
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.365-367
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• 2010

In this paper, we presented the exact Riemann solver for the air-water two-phase shock tube problems where the strength of the propagated sock wave is moderately weak. The shock tube has a diaphragm in the middle which separates water medium in the left and air medium in the right. By rupturing the diaphragm, various waves such as rarefaction wave, shock wave and contact discontinuity are propagated into water and air. Both fluids are treated as compressible, with the linearized equations of state. We used the isentropic relations for the air and water assuming a weak shock wave. We solved the shock tube problem considering a high pressure in the water and a low pressure in the air. The numerical results cleary showed a left-traveling rarefaction wave in the water, a right-traveling shock wave in the air, and the right-traveling material interface.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.699-715
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• 2024

We study the Riemann problem for the pressureless Euler system with the source term depending on the time. By means of the variable substitution, two kinds of Riemann solutions including deltashock and vacuum are constructed. The generalized Rankine-Hugoniot relation and entropy condition of the delta-shock are clarified. Because of the source term, the Riemann solutions are non-self-similar. Moreover, we propose a time-dependent viscous system to show all of the existence, uniqueness and stability of solutions involving the delta-shock by the vanishing viscosity method.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.215-220
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• 2008

A numerical method for gas-liquid two-phase flow is applied to solve shock-bubble interaction problems. The present method employs a finite-difference Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. By this method, a Riemann problem for shock tube was computed for validation. Then, shock-bubble interaction problems between cylindrical bubbles located in the liquid and incident liquid shock wave are computed.

• 한국전산유체공학회:학술대회논문집
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• 2007.10a
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• pp.249-257
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• 2007

A high resolution numerical method aimed at solving gas-liquid two-phase flow is proposed and applied to gas-liquid two-phase shock tube problem. The present method employs a finite-difference 4th-order Runge-Kutta method and Roe's flux difference splitting approximation with the MUSCL TVD scheme. By applying the homogeneous equilibrium cavitation model, the present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation and large density changes. The speed of sound for gas-liquid two-phase media is derived on the basis of thermodynamic relations and compared with that by eigenvalues. By this method, a Riemann problem for Euler equations of one dimensional shock tube was computed. Numerical results such as detailed observations of shock and expansion wave propagations through the gas-liquid two-phase media and some data related to computational efficiency are made. Comparisons of predicted results and exact solutions are provided and discussed.

• Journal of Korea Water Resources Association
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• v.37 no.10
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• pp.845-855
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• 2004

The propagation and associated run-up process of nearshore tsunamis in the vicinity of shorelines have been analyzed by using a two-dimensional numerical model. The governing equations of the model are the nonlinear shallow-water equations. They are discretized explicitly by using a finite volume method and the numerical fluxes are reconstructed with a HLLC approximate Riemann solver and weighted averaged flux method. The model is applied to two problems; The first problem deals with water surface oscillations, while the second one simulates the propagation and subsequent run-up process of nearshore tsunamis. Predicted results have been compared to available analytical solutions and laboratory measurements. A very good agreement has been observed.