• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.2
• /
• pp.467-474
• /
• 1993

Viscous flow and heat transfer phenomena in an axisymmetric cylinder which models a diesel engine have been numerically studied. In order to search for a way to minimize numerical diffusion, the effectiveness and the appropriateness of two selected numerical schemes for convective terms in the governing equations have been tested. They are Linear Upwind Difference Scheme and Hybrid Scheme. Using a standard k-.epsilon. turbulence model, the calculation has been carried out basically up to 180.deg. of crank angle. As a result, it was shown from comparison with previous experimental data that Linear Upwind Difference Scheme is less influenced than Hybrid Scheme by the numerical diffusion and it was suggested that these effects of numerical diffusion can be more significant than those due to turbulence modeling.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.05b
• /
• pp.1063-1067
• /
• 2005

A second-order accuracy upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with field observed data and results of a first-order accuracy upwind scheme, In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water The target events is 1993 Hokktaido Nansei Oki Tsunami. The predicted results represent reasonably the run-up heights of tsunamis in the East Sea. And, The results of simulation is used to design inundation map.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.1
• /
• pp.1-21
• /
• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Journal of Korea Water Resources Association
• /
• v.38 no.6 s.155
• /
• pp.461-469
• /
• 2005

A second-order upwind scheme is used to investigate the run-up heights of tsunamis in the East Sea and the predicted results are compared with the field data and results of a first-order upwind scheme. In the numerical model, the governing equations solved by the finite difference scheme are the linear shallow-water equations in deep water and nonlinear shallow-water equations in shallow water. The target events are 1983 Central East Sea Tsunami and 1993 Hokkaido Nansei Oki Tsunami. The predicted results represent reasonably well the run-up heights of tsunamis in the East Sea. And, the results of simulation are used for the design of inundation map.

• 유체기계공업학회:학술대회논문집
• /
• 2000.12a
• /
• pp.285-292
• /
• 2000

Numerical calculation is applied to centrifugal pump at design condition by using commercial code STAR-CD and Tascflow, and these results are compared with experimental data at impeller outlet. Numerical analysis is also performed by changing turbulence model and discretization scheme at design condition using Tascflow. Turbulence model and discretization scheme used to Tascflow are k-$\epsilon$, k-$\omega$ turbulence model and upwind, modified linear profile scheme. W;th the same turbulence model and discretization scheme, two results of STAR-CD and Tascflow are very similar. But there is significant difference in numerical results near hub and shroud of impeller with different kinds of turbulent model and discretization scheme at design condition. And with k- $\omega$ turbulence model and modified linear profile scheme, it is showed that numerical results are very similar to experimental results of impeller outlet

• 한국방재학회:학술대회논문집
• /
• 2008.02a
• /
• pp.431-434
• /
• 2008

Pratical dispersion-correction scheme is applicated to simulate the distant propagation of tsunami. This scheme is based on the leap-frog finite difference scheme for the linear shallow-water equations. The new scheme has the advantage of using the constant spatial grid size and time step size even in area of variable depths. And this new model constructed by using the 2nd upwind scheme, dynamic linking method, and staggered grid system. This model is simulated to near Sokcho harbor about The Central East Sea Tsunami in 1983. And this result is compared to tide gage and result of former model.

• International Journal of Aeronautical and Space Sciences
• /
• v.3 no.1
• /
• pp.74-85
• /
• 2002

The numerical experiment has been conducted to investigate the unsteady shock wave reflecting phenomena. The cell-vertex finite-volume, Roe's upwind flux difference splitting method with unstructured grid is implemented to solve unsteady Euler equations. The $4^{th}$-order Runge-Kutta method is applied for time integration. A linear reconstruction of the flux vector using the least-square method is applied to obtain the $2^{nd}$-order accuracy for the spatial derivatives. For a better resolution of the shock wave and slipline, the dynamic grid adaptation technique is adopted. The new concept of grid adaptation technique, which is much simpler than that of conventional techniques, is introduced for the current study. Three error indicators (divergence and curl of velocity, and gradient of density) are used for the grid adaptation procedure. Considering the quality of the solution and the numerical efficiency, the grid adaptation procedure was updated up to $2^{nd}$ level at every 20 time steps. For the convenience of comparison with other experimental and analytical results, the case of interaction between the straight incoming shock wave and a sharp wedge is simulated for various flow conditions. The numerical results show good agreement with other experimental and analytical results, in the shock wave reflecting structure, slipline, and the trajectory of the triple points. Some critical cases show disagreement with the analytical results, but these cases also have been proven to show hysteresis phenomena.

• Journal of the Society of Naval Architects of Korea
• /
• v.33 no.3
• /
• pp.35-47
• /
• 1996

A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.