• Journal of Korea Water Resources Association
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• v.32 no.2
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• pp.185-195
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• 1999

The finite difference method and the method of characteristics are frequently used for the numerical analysis of kinematic wave model. Truncation errors cause the peak discharge dissipated in the solution from the finite difference method. The peak discharge is conserved in the solution from the finite difference method. The peak discharge is conserved in the solution from the method of characteristics, however, the shock may deteriorates the numerical solution. In this paper, distinctive features of each scheme are investigated for the numerical analysis of kinematic wave model, and applicability of shock fitting algorithm such as Propagating Shock Fitting and Approximated Shock Fitting methods are studied. Propagating Shock Fitting method appears to treat shock properly, however, it failed to fit the shock appropriately when applied to a sudden inflow change in a long river. Approximate Shock Sitting method, which uses finer elements, is found to be more proper shock-fitting than the Propagating Shock Fitting method. Comparisons are made between two solution from the kinematic wave theory with shock fitting and full dynamic wave theory, and the results are discussed.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.685-695
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• 2020

In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

• Journal of the Korean Society of Combustion
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• v.1 no.1
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• pp.83-91
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• 1996

A numerical study is carried out to examine the ignition and propagation process of detonation wave in SCRam-accelerator operating in superdetonative mode. The time accurate solution of Reynolds averaged Navier-Stokes equations for chemically reacting flow is obtained by using the fully implicit numerical method and the higher order upwind scheme. As a result, it is clarified that the ignition process has its origin to the hot temperature region caused by shock-boundary layer interaction at the shoulder of projectile. After the ignition, the oblique detonation wave is generated and propagates toward the inlet while constructing complex shock-shock interaction and shock-boundary layer interaction. Finally, a standing oblique detonation wave is formed at the conical ramp.

• International Journal of Aeronautical and Space Sciences
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• v.3 no.1
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• pp.74-85
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• 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 applied mathematics & informatics
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• v.10 no.1_2
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• pp.119-130
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• 2002

An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.441-457
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• 2005

An analytical method is presented to solve the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere subjected to thermal shock and electric excitation. Exact expressions for the transient responses of displacements, stresses, electric displacement and electric potentials in the piezoelectric hollow sphere are obtained by means of Hankel transform, Laplace transform, and inverse transforms. Using Hermite non-linear interpolation method solves Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between thermo-elastic field and thermo-electric field. Thus, an analytical solution for the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere is obtained. Finally, some numerical results are carried out, and may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.32 no.11
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• pp.832-840
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• 2008

Ablation occurs at irradiance beyond $10^9\;W/cm^2$ with nanosecond and short laser pulses focused onto any materials. Phenomenologically, the surface temperature is instantaneously heated past its vaporization temperature. Before the surface layer is able to vaporize, underlying material will reach its vaporization temperature. Temperature and pressure of the underlying material are raised beyond their critical values, causing the surface to explode. The pressure over the irradiated surface from the recoil of vaporized material can be as high as $10^5\;MPa$. The interaction of high power nanosecond laser with a thin metal in air has been investigated. The nanosecond pulse laser beam in atmosphere generates intensive explosions of the materials. The explosive ejection of materials make the surrounding gas compressed, which form a shock wave that travels at several thousand meters per second. To understand the laser ablation mechanism including the heating and ionization of the metal after lasing, the temporal evolution of shock waves is captured on an ICCD camera through laser flash shadowgraphy. The expansion of shock wave in atmosphere was found to agree with the Sedov's self-similar spherical blast wave solution.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.115-119
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• 2009

We numerically investigated propagation of various waves in the two-phase flows such as sound wave, shock wave, rarefaction wave, and contact discontinuity in terms of pressure, void fraction, velocity and density of the two phases. The waves have been generated by a hydrodynamic shock tube, a pair of symmetric impulsive expansion, impulsive pressure and impulsive void waves. The six compressible two-fluid two-phase conservation laws with interfacial friction terms have been solved in two fractional steps. The first PDE Operator is solved by the HLL scheme and the second Source Operator by the semi-implicit stiff ODE solver. In the HLL scheme, the fastest wave speeds were estimated by the analytic eigenvalues of an approximate Jacobian matrix. We have discussed how the interfacial friction terms affect the wave structures in the numerical solution.

• Structural Engineering and Mechanics
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• v.59 no.5
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• pp.841-852
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• 2016

The present paper is concerned with the investigation of propagation of thermoelastic media, the finite difference technique is used to obtain the solution for the uncoupled dynamic thermoelastic stress problem in a non-homogeneous orthrotropc thick cylindrical shell. In implementing the method, the linear dynamic thermoelasticity equations are used with the appropriate boundary and initial conditions. Thermal shock stress becomes of significant magnitude due to stress wave propagation which is initiated at the boundaries by sudden thermal loading. Numerical results have been given and illustrated graphically in each case considered. The presented results indicate that the effect of inhomogeneity is very pronounced.

• Journal of the Korean Chemical Society
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• v.42 no.4
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• pp.398-410
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• 1998

For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.