• 한국전산유체공학회:학술대회논문집
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• 2001.05a
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• pp.99-104
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• 2001

This paper deals with the development of shock stable scheme that is free from shock instability. Roe's FDS is known to preserve good accuracy but to suffer from shock instability, i.e. the carbuncle phenomenon. As the first step toward the shock stable scheme, Roe's FDS is compared with HLLE scheme to identify the source of shock instability. Then control function f is introduced into the pressure term in Roe's FDS to cure shock instability. Various numerical tests concerned with shock instability are performed to demonstrate the shock stability of the proposed scheme.

• Journal of The Korean Astronomical Society
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• v.17 no.2
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• pp.115-125
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• 1984

Effect of magnetic field on the thermal instability is studied in the radiatively cooling region behind an interstellar shock of moderate propagation velocity (${\sim}10\;km/sec$). It is shown that the presence of interstellar magnetic field of a few micro gauss is very effective in preventing the thermal instability from building-up density concentration. In the absence of magnetic field, the shock-induced thermal instability amplifies preshock density inhomogeneity by more than an order of magnitude. However, in the presence of magnetic field, the amplified density contrast is shown to be only a factor 2.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.191-203
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• 2011

The interface between fluids of different densities is unstable under acceleration by a shock wave. A previous small amplitude linear theory for the compressible Euler equation failed to provide a quantitatively correct prediction for the growth rate of the unstable interface. In this paper, to include dominant nonlinear effects in a large amplitude regime, we present high-order perturbation equations of the Euler equation, and boundary conditions for the contact interface and shock waves.

• Journal of the Korean Society of Combustion
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• v.7 no.1
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• pp.23-30
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• 2002

Instability of oblique detonation waves (ODW) at off-attaching condition was investigated through a series of numerical simulations. Two-dimensional wedge of finite length was considered in $H_2/O_2/N_2$ mixtures at superdetonative condition. Numerical simulation was carried out with a compressible fluid dynamics code and a detailed hydrogen-oxygen combustion mechanism. Present result reveals that there is a chemical kinetic limit of the ODW detachment, in addition to the theoretical limit predicted by Rankine-Hugoniot theory with equilibrium chemistry. Result also presents that ODW still attaches at a wedge as an oblique shock-induced flame showing periodically unstable motion, if the Rankine-Hugoniot limit of detachment is satisfied but the chemical kinetic limit is not. Mechanism of the periodic instability is considered as interactions of shock and reaction waves coupled with chemical kinetic effects. From the investigation of characteristic chemical time, condition of the periodic instability is identified as follows; at the detaching condition of the Rankine-Hugoniot theory, (1) flow residence time is smaller than the chemical characteristic time, behind the detached shock wave with heat addition, (2) flow residence time should be greater than the chemical characteristic time, behind an oblique shock wave without heat addition.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.37.2-37.2
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• 2014

Gas in disk galaxies interacts nonlinearly with a underlying stellar spiral potential to form galactic spiral shocks. Numerical simulations typically show that these shocks are unstable to the wiggle instability, forming non-axisymmetric structures with high vorticity. While previous studies suggested that the wiggle instability may arise from the Kelvin-Helmholtz instability or orbit crowding of gas elements near the shock, its physical nature remains uncertain. It was even argued that the wiggle instability is of numerical origin, caused by the inability of a numerical code to resolve a shock that is inclined to numerical grids. In this work, we perform a normal-mode linear stability analysis of galactic spiral shocks as a boundary-value problem. We find that the wiggle instability originates physically from the potential vorticity generation at a distorted shock front. As the gas follows galaxy rotation, it periodically passes through multiple shocks, successively increasing its potential vorticity. This sets up a normal-mode that grows exponentially, with a growth rate comparable to the orbital angular frequency. We show that the results of our linear stability analysis are in good agreement with the those of local hydrodynamic simulations of the wiggle instability.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.155-172
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• 2000

Mode interactions at Unstable fluid interfaces induced by a shock wave (Richtmyer-Meshkov Instability) are studied both analytically and numerically. The analytical approach is based on a potential flow model with source singularities in incompressible fluids of infinite density ratio. The potential flow model shows that a single bubble has a decaying growth rates at late time and an asymptotic constant radius. Bubble interactions, bubbles of different radii propagates with different velocities and the leading bubbles grow in size at the expense of their neighboring bubbles, are predicted by the potential flow model. This phenomenon is validated by full numerical simulations of the Richtmyer-Meshkov instability in compressible fluids for initial multi-frequency perturbations on the unstable interface.

• Advances in aircraft and spacecraft science
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• v.6 no.1
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• pp.19-30
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• 2019

Two- and three-dimensional turbulent airflows in a 9-degrees-bent channel are studied numerically. The inner surfaces of upper and lower walls are parallel to each other upstream and downstream of the bend section. The free stream is supersonic, whereas the flow at the channel exit is either supersonic or subsonic depending on the given backpressure. Solutions of the Reynolds-averaged Navier-Stokes equations are obtained with a finite-volume solver ANSYS CFX. The solutions reveal instability of formed shock waves and a flow hysteresis in considerable bands of the free-stream Mach number at zero and negative angles of attack. The instability is caused by an interaction of shocks with the expansion flow formed over the convex bend of lower wall.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.52.2-52.2
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• 2020

At quasi-perpendicular shocks in the high-�� (��=Pgas/Pmag~100) intracluster medium (ICM), various microinstabilities occur by the temperature anisotropies and/or drift motions of plasma. In the downstream, the Alfvén ion cyclotron instability (AIC) due to the ion temperature anisotropy (Ti⊥>Ti║) is triggered by shock-reflected ions, the whistler instability (WI) is driven by the electron temperature anisotropy (Te⊥>Te║) as a consequence of the shock compression of magnetic fields, and the mirror instability is generated due to the ion and/or electron temperature anisotropy. At the shock foot, the modified two stream instability (MTSI) is possibly excited by the cross-field drift between ions and electrons. In the upstream, electron firehose instability (EFI) is driven by the electron temperature anisotropy or the relative drift between incoming and reflected electrons. These microinstabilities play important roles in the particle acceleration in ICM shocks, so understanding of the microinstabilities and the resultant plasma waves is essential. In this study, based on a linear stability analysis, the basic properties of the microinstabilities in ICM shocks and the ion/electron scale fluctuations are described. We then discuss the implication of our work on the electron pre-acceleration in ICM shocks.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.55.2-55.2
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• 2019

The firehose instability is driven by a pressure anisotropy in a magnetized plasma when the temperature along the magnetic field is higher than the perpendicular temperature. Such condition occurs commonly in astrophysical and space environments, for instance, when there are beams aligned with the background magnetic field. Recently, it was argued that, in weak quasi-perpendicular shocks in the high-β intracluster medium (ICM), shock-reflected electrons propagating upstream cause the temperature anisotropy. This electron temperature anisotropy can trigger the electron firehose instability (EFI), which excites oblique waves in the shock foot. Scattering of electrons by these waves enables multiple cycles of shock drift acceleration (SDA) in the preshock region, leading to the electron injection to diffusive shock acceleration (DSA). In the study, the kinetic properties of the EFI are examined by the linear stability analysis based on the kinetic Vlasov-Maxwell theory and then further investigated by 2D Particle-in-Cell (PIC) simulations, especially focusing on those in high-β (β~100) plasmas. We then discuss the basic properties of the firehose instability, and the implication of our work on electron acceleration in ICM shock.

• The Journal of Korean Physical Therapy
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• v.34 no.3
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• pp.91-97
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• 2022

Purpose: This study investigated the short-term effectiveness of extracorporeal shock wave therapy (ESWT) on pain, the ankle instability, the ankle function, dorsiflexion range of motion (ROM), and dynamic balance in patients with chronic ankle instability (CAI). Methods: Eighteen participants were divided into an experimental (n=9) and control group (n=9). The ESWT in the experimental group was applied to the lateral collateral ligament in combination with the tibialis anterior whereas the ESWT was applied to the lateral collateral ligament of the ankle alone in the control group. Pain, the ankle instability, the ankle function, dorsiflexion ROM, and dynamic balance were measured using the Visual analog scale, Cumberland ankle instability tool, American Orthopedic Foot and Ankle Society ankle-hindfoot score, weight-bearing lunge, and Y-balance test, before and after ESWT intervention. Results: Significant interactions (group × time) and time effects were observed in the dorsiflexion ROM and dynamic balance. Bonferroni's post-hoc analysis showed that the experimental group revealed a more significant change in dorsiflexion ROM and dynamic balance than the control group. There was a significant time effect in the pain, the ankle instability, and the ankle function, but no significant interaction (group × time) was observed. Conclusion: The ESWT could improve the pain, ankle instability, ankle function, dorsiflexion ROM, and dynamic balance in patients with CAI. Furthermore, the ESWT combined with lateral ankle ligaments and tibialis anterior more improves the dorsiflexion ROM and dynamic balance.