• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1998.04a
• /
• pp.392-398
• /
• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• International Journal of Aeronautical and Space Sciences
• /
• v.6 no.1
• /
• pp.1-7
• /
• 2005

The inlet boundary condition of computations about the supersonic turbine flow is commonly applied as far-field inlet boundary condition with specified velocity. However, the inflow condition of supersonic turbine is sometimes affected by the shocks or expansion waves propagated from leading edges of blade. These shocks and expansion waves alter the inlet boundary condition. In this case, the inlet boundary condition can not be specified Therefore, in this paper, numerical analyses for three different inlet conditions - fa-field inlet boundary condition, inlet boundary condition with a linear nozzle and inlet boundary condition with a converging-diverging nozzle - have been performed and compared with experimental results to solve the problem. It is found that the inlet condition with a linear nozzle or a converging-diverging nozzle can prevent changing of inlet boundary condition, and thus predict more accurately the supersonic flow within turbine cascade than a far-field inlet boundary condition does.

• Journal of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.465-477
• /
• 2023

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

• Journal of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.319-330
• /
• 2002

The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.09b
• /
• pp.902-903
• /
• 2005

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.35 no.2
• /
• pp.41-48
• /
• 2023

In this study, simplified linear numerical method that can simulate wave generation and transformation by a moving bottom is introduced. Numerical analysis is conducted in wave number domain after continuity equation, linear dynamic and kinematic free surface boundary conditions and linear kinematic bottom boundary condition are Fourier transformed, and the results are expressed in space domain by an inverse Fourier transform. In the wavenumber domain, the dynamic free water surface boundary condition and the kinematic free water surface boundary condition are numerically calculated, and the velocity potential in the mean water level (z = 0) satisfies the continuity equation and the kinematic bottom boundary condition. Wave generation and transformation are investigated when the triangular and rectangular shape of bottoms move periodically. The results of the simplified numerical method are compared with the results of previous analytical solutions and agree well with them. Stability of numerical results according to the calculation time interval (Δt) and the calculation wave number interval (Δk) was also investigated. It was found that the numerical results were appropriate when Δt ≤ T(period)/1000 and Δk ≤ π/100.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.1
• /
• pp.19-30
• /
• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.3
• /
• pp.179-202
• /
• 2019

This paper presents second derivative generalized extended backward differentiation formulas (SDGEBDFs) based on the second derivative linear multi-step formulas of Cash [1]. This class of second derivative linear multistep formulas is implemented as boundary value methods on stiff problems. The order, error constant and the linear stability properties of the new methods are discussed.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2003.10a
• /
• pp.99-103
• /
• 2003

An analysis of the flow within supersonic turbine cascades is necessary to design and manufacture turbo-pump system. Because of the differences between the specified inlet boundary value and the computed inlet value caused by the far field inlet boundary condition, the computations at desired inlet conditions can not be achieved. So, this paper studied the problem occurred when far field inlet conditions were specified as inlet boundary conditions. And the numerical analyses using Fine Turbo, CFD Program, has been performed and compared with those of experiments when a converging-diverging nozzle or a linear nozzle was located in front of cascades instead of the far field inlet condition.

• Coupled systems mechanics
• /
• v.4 no.1
• /
• pp.1-18
• /
• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.