• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.1
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• pp.1-11
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• 2010

The definition of the speed of sound is reexamined since it is crucial in the numerical analysis of compressible real gas flows. The thermodynamic speed of sound (TSS), $a_{th}$, and the characteristic speed of sound (CSS), $a_{ch}$, are derived using generalized equation of state (EOS). It is found that the real gas EOS, for which pressure is not linearly dependent on density and temperature, results in slightly different TSS and CSS. in this formalism, Roe's approximate Riemann solver was derived again with corrections for real gases. The results show a little difference when the speeds of sound are applied to the Roe's scheme and Advection Upstream Splitting Method (AUSM) scheme, but a numerical instability is observed for a special case using AUSM scheme. It is considered reasonable to use of CSS for the mathematical consistency of the numerical schemes. The approach is applicable to multi-dimensional problems consistently.

• Fire Science and Engineering
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• v.24 no.5
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• pp.32-38
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• 2010

Multi-dimensional fire dynamics were studied numerically with the change in ventilation conditions in a full-scale ISO 9705 room. Fire Dynamic Simulator (FDS) was used for the identical conditions conducted in previous experiments. Flow rate and doorway width were changed to create over-ventilated fire (OVF) and under-ventilated fire (UVF). From the numerical simulation, it was found that the internal flow pattern rotated in the opposite direction for the UVF relative to the OVF so that a portion of products recirculated to the inside of compartment. Significant change in flow pattern with ventilation conditions may affect changes in the complex process of CO and soot formation inside the compartment due to increase in the residence time of high-temperature products. The fire behavior in the UVF created complex 3D characteristics of species distribution as well as thermal and flow structures. In particular, additional burning near the side wall inside the compartment significantly affected the flow pattern and CO production. The distribution of CO inside the compartment was explained with 3D $O_2$ distribution and flow patterns. It was observed that gas sampling at local positions in the upper layer were insufficient to completely characterize the internal structure of the compartment fire.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.563-585
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• 2008

This paper presents how to improve the efficiency and accuracy in the pricing and sensitivity evaluation for derivatives, since the need for the evaluation of complicated derivatives is increased. The Monte Carlo(MC) simulation using the quasi random number instead of pseudo random number can improve the elapsed time and accuracy for the valuation of European-type derivatives. However, the quasi MC simulation method has its limit for applying it in the multi-dimensional case such as American-type and path-dependent options due to the increased correlation between dimensions as the dimension of random numbers is increased. In order to complement this problem, we develop a modified method in which correlation values are controlled to be below a pre-specified value. Thus, this method is applicable for the pricing of either derivatives ill which underlying assets or risk factors are several or derivatives having path-dependent or early redemption property. Furthermore, we illustrate that it is important to take an appropriate grid interval for the use of finite difference method(FDM) by applying the FDM to one example of non-symmetrical butterfly spreads.