• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.209-219
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• 2013

The present paper deals with the extension of AUSMPW+ scheme into two-fluid model for multiphase flow. AUSMPW+ scheme is the improvement of a single-phase AUSM+ scheme by designing pressure-based weighting functions to prevent oscillations near a wall and shock instability after a strong shock. Recently, Kitamura and Liou assessed a family of AUSM-type schemes with two-fluid model governing equations [K. Kitamura and M.-S. Liou, Comparative study of AUSM-Family schemes in compressible multi-phase flow simulations, ICCFD7-3702 (2012)]. It was observed that the direct application of the single-phase AUSMPW+ did not provide satisfactory results for most of numerical test cases, which motivates the current study. It turns out that, by designing pressure-based weighting functions, which play a key role in controlling numerical diffusion for two-fluid model, problems reported in can be overcome. Various numerical experiments validate the proposed modification of AUSMPW+ scheme is accurate and robust to solve multiphase flow within the framework of two-fluid model.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.29-34
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• 1999

A two-dimensional Navier-Stokes code based on AUSMPW+ scheme has been developed to simulate the hypersonic flowfield of hypersonic shock-shock interaction. AUSMPW+ scheme is a new hybrid flux splitting scheme, which is improved by introducing pressure-based weight functions to eliminate the typical drawbacks of AUSM-type schemes, such as non-monotone pressure solutions. To study the real gas effects, three different gas models are taken into account in this paper: perfect gas, equilibrium flow and nonequilibrium flow. It has been investigated how each gas model influences on the peak surface loading, such as wall pressure and wall heat transfer, and unsteady flowfield structure in the region of shock-shock interaction. With the results, the value of peak pressure is not sensitive to the real gas effects nor to the wall catalyticity. However, the value of peak heat transfer rates is affected by the real gas effects and the wall catalyticity. The structure of the flowfield also changes drastically in the presence of real gas effects.

• International Journal of Aeronautical and Space Sciences
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• v.1 no.1
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• pp.21-28
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• 2000

The flowfield of hypersonic shock-shock interaction has been simulated using a two-dimensional Navier-Stokes code based on AUSMPW+ scheme. AUSMPW+ scheme is a new hybrid flux splitting scheme, which is improved by introducing pressure-based weight functions to eliminate the typical drawbacks of AUSM-type schemes, such as non-monotone pressure solutions. To study the real gas effects, three different gas models are taken into account in the present paper: perfect gas, equilibrium flow and non equilibrium flow. It has been investigated how each gas model influences on the peak surface loading, such as wall pressure and wall heat transfer, and unsteady structure of flowfield in the region of shock-shock interaction. With the results, the value of peak pressure is not sensitive to the real gas effects nor to the wall catalyticity. However, the value of peak heat transfer rates is affected by the real gas effects and the wall catalyticity. Also, the structure of the flowfield changes drastically in the presence of real gas effects.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.9
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• pp.12-26
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• 2004

A new treatment of cell-interface flux in AUSM-type methods is introduced to reduce the numerical dissipation. Through analysis of TVD limiters, a criterion for the more accurate prediction of cell-interface state is found out and M-AUSMPW+ is developed by determining the transferred property newly and appropriately within the criterion. The superiority of M-AUSMPW+ is clearly revealed in multi-dimensional flow problems. It can eliminate numerical dissipation effectively in a non-flow aligned grid system. As a result, M-AUSMPW+ is shown to be much more accurate and effective than other previous schemes in multi-dimensional problems. Through a stationary contact discontinuity, a vortex flow, a shock wave/boundary layer interactions and viscous shock tube problems, it is verified that accuracy of M-AUSMPW+ is improved.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.13-17
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• 2006

RoeM and AUSMPW+ schemes are two of the most accurate and efficient schemes which are recently developed for the analysis of single phase gas dynamics. In this paper, we developed two-phase versions of these schemes for the analysis of gas-liquid large density ratio two-phase flow. We adopt homogeneous equilibrium model (HEM) using mass fraction to describe different two phases. In the Eulerian-Eulerian framework, HEM assumes dynamic and thermal equilibrium of the two phases in the same computational mesh. From the mixture equation of state (EOS), we derived new shock-discontinuity sensing term (SDST), which is commonly used in RoeM and AUSMPW+ for the stable numerical flux calculation. The proposed two-phase versions of RoeM and AUSMPW+ schemes are applied on several air-water two-phase test problems. In spite of the large discrepancy of material properties such as density, enthalpy, and speed of sound, the numerical results show that both schemes provide very satisfactory solutions.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.2
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• pp.21-29
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• 2002

The M-AUSMPW+ scheme that can capture shock waves exactly with monotonic characteristic is developed by analyzing the cause of oscillation in shock regions. Firstly shock-capturing characteristics of general FVS including the AUSM-type schemes are investigated in detail, according to the different between a cell-interface and a sonic transition position. The cause of oscillation is the improper numerical dissipation that could not represent the real physics. The M-AUSMPW+ could capture shocks exactly without oscillatory behaviors in considering the sonic transition position and an cell-interface position

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.103-108
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• 2002

The M-AUSMPW+ scheme that can capture shock waves exactly with monotonic characteristics is modifided from AUSMPW+ by analyzing the cause of oscillation in shock regions. Firstly shock-capturing characteristics of general FVS including the AUSM-type schemes are investigated in detail, according to the difference between a cell-interface and a sonic transition position. The cause of oscillation is the improper numerical dissipation that could not represent the real Physics. The M-AUSMPW+ could capture shocks exactly without oscillatory behaviors in considering the sonic transition position and an cell-interface position.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.2
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• pp.30-38
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• 2002

The monotonic characteristics of AUSM-type shemes are proven by mathmatics and numerics. Qualitatively well-known characteristics are quantified by mathematics and the magnitude of oscillatory behaviors of each schemes could be compared directly. Moreover, it is also studied how the sonic transition position affects the oscillation in capturing the shocks. Lastly M-AUSMPW+, the latest improved AUSM-type scheme, is shown to have monotonic characeristics though all shock conditions.

• 한국전산유체공학회:학술대회논문집
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• 2003.08a
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• pp.5-10
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• 2003

In order to reduce the excessive numerical dissipation, the new spatial discretization scheme is introduced. The present method in this paper has the formula that has an additional procedure of defining transferred properties at a cell-interface, based on AUSMPW+. The newly defined transferred property could eliminate numerical dissipation effectively in non-flow aligned grid system. In addition, the present method guarantees the monotonic characteristic in capturing a discontinuity. Through a stationary or moving contact discontinuity and a stationary or moving shock discontinuity, a vortex discontinuity and shock wave/ boundary layer interaction, it is verified that the accuracy of the present method is improved.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.47-52
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• 2002

The supersonic flow around multi-stage rocket system is analyzed using 3-D compressible unsteady flow solver. A Chimera overset grid technique is used for the calculation of present configuration and grid around the core rocket is composed of 3 zones to represent fins in the core rocket. Flow solver is parallelized to reduce the computation time, and an efficient parallelization algorithm for Chimera grid technique is proposed. AUSMPW+ scheme is used for the spatial discretization and LU-SGS for the time integration. The flow field around multi-stage rocket was analyzed using this developed solver, and the results were compared with that of a sequential solver The speed-up ratio and the efficiency were measured in several processors. As a result, the computing speed with 12 processors was about 10 times faster than that of a sequential solver. Developed flow solver is used to predict the trajectory of booster in separation stage. From the analyses, booster collides against core rocket in free separation case. So, additional jettisoning forces and moments needed for a safe separation are examined.