• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.995-1006
• /
• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a dynamic analysis. Large eddy simulation of isotropic turbulence is performed with various dissipative and non-dissipative schemes to investigate the effect of numerical dissipation on the resolved solutions. It is shown by the present dynamic analysis that upwind schemes reduce the aliasing error and increase the finite differencing error. The existence of optimal upwind scheme that minimizes total numerical error is verified. It is also shown that the finite differencing error from numerical dissipation is the leading source of numerical errors by upwind schemes. Simulations of a turbulent channel flow are conducted to show the existence of the optimal upwind scheme.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.973-983
• /
• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes is evaluated for large eddy simulation of turbulent flow. Two turbulent flows are considered: turbulent channel flow at Re = 23000 and flow over a circular cylinder at Re = 3900. The effects of numerical dissipation on the finite differencing and aliasing errors and the subgrid-scale stress are investigated. It is shown through the simulations that compact upwind schemes are not suitable for LES, whereas the fourth order-compact centered scheme is a good candidate for LES provided that proper dealiasing of nonlinear terms is performed. The classical issue on the aliasing error and the treatment of nonlinear terms is revisited with compact difference schemes.

• Journal of computational fluids engineering
• /
• v.11 no.1 s.32
• /
• pp.36-42
• /
• 2006

The existing numerical approximations of convection flux, especially the spatial higher-order difference schemes, in unstructured cell-centered finite volume methods are examined in detail with each other and evaluated with respect to the accuracy through their application to a 2-D benchmark problem. Six higher-order schemes are examined, which include two second-order upwind schemes, two central difference schemes and two hybrid schemes. It is found that the 2nd-order upwind scheme by Mathur and Murthy(1997) and the central difference scheme by Demirdzic and Muzaferija(1995) have more accurate prediction performance than the other higher-order schemes used in unstructured cell-centered finite volume methods.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.20 no.11
• /
• pp.3589-3597
• /
• 1996

The Reynolds-averaged Navier-Stokes equations with the equations of the k-.epsilon. turbulence model are solved numerically in a general curvilinear system for a three-dimensional turbulent flow around an Ahmed body. The simulation is especially aimed at the evaluation of three finite differencing schemes for the convection term, which include the upwind differencing scheme(UDS), the second order upwind differencing scheme(SOU scheme) and the QUICK scheme. The drag coefficient, the velocity and pressure fields are found to be changed considerably with the adopted finite differencing schemes. It is clearly demonstrated that the large difference between computation and experiment in the drag coefficient is due to relatively high predicted values of pressure drag from both front part and vertical rear end base. The results also show that the simulation with the QUICK or SOU scheme predicts fairly well the flow field and gives more accurate drag coefficient than other finite differencing scheme.

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.984-994
• /
• 2003

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a spectral, static error analysis. To investigate the effect of numerical dissipation on LES solutions, power spectra of discretization errors are evaluated for isotropic turbulence models in both continuous and discrete wavevector spaces. Contrary to the common belief, the aliasing errors from upwind-biased schemes are larger than those from comparable non-dissipative schemes. However, this result is the direct consequence of the definition of the power spectral density of the aliasing error, which poses the limitation of the static error analysis for upwind schemes.

• Journal of Korea Water Resources Association
• /
• v.38 no.2
• /
• pp.155-166
• /
• 2005

Upwind schemes are very well adapted to the discontinuous flow and have become popular for applications Involving dam break flow, transcritical Slow, etc. However, upwind schemes have been applied mainly to the idealized problems not to the natural channels with irregular geometry so far because of the error due to source terms. In this paper, the new type of upwind discretization of source terms, which uses the normalized Jacobian to discretize the source terms, is proposed. As results of tests to flows with source terms by the upwind models, the method proposed in this paper is proved as efficient and accurate. This generalized method for differencing source terms is simple and might beapplicable to diverse type of flux upwind discretization scheme in finite difference method.

• 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 computational fluids engineering
• /
• v.4 no.1
• /
• pp.41-52
• /
• 1999

이 논문에서는, QUICK해법의 불안정성을 개량하므로써, 수치계산에 있어서 수렴이 빠르고, 수치적으로 안정한 계산을 할 수 있는 새로운 MQUICK 상류해법을 제안하고, 이를 비압축성 층류유동의 계산에 적용하였다. 또한, 해법의 정확성, 안정성, 수렴속도에 대한 검토를 통하여 본 MQUICK 상류해법의 유효성과 타당성이 평가되었다. 이 해법에서는 인공산일의 가감을 조절하기 위하여 가중계수 α를 써서 정식화 하였고, 위의 검토를 통하여 α의 최적값을 조사하였다. 이 해법을 SMAC 음해법에 적용하여 2 차원 공동유동, 3 차원 덕트유동과 같은 몇몇 표준문제를 계산하고, 계산된 결과를 실험값 또는, 3 차 정확도의 상류해법 및 QUICK해법에 의한 결과 들과 비교 하므로써, 본 MQUICK 상류해법이 위의 다른 해법에 비하여 안정하고, 유효성이 높은 해법임을 확인 하였다.

• 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.