• Journal of Korean Society for Atmospheric Environment
• /
• v.12 no.5
• /
• pp.577-585
• /
• 1996

A screening study was performed in order to resolve the flow, combustion and emission characteristics of the gas furmace with co-axial diffusion flane burner. A control-valume based finite-difference method with the power-law scheme was employed for discretization. Numerical procedure for the differential equation was used by SIMPLEST to enclosute rapid converge. A k-.varepsilon. model was incorporated for the closure of turbulence. The mass fraction and mixture fraction were calculated by cinserved scalar method. An equilibrium analysis was employed to determine the concentration of radicals in the product stream and conserbation equations were them solved for N amd NO by Zelovich reaction scheme. The method was exercised in a simple one-dimensional case first, to determine the effects of air ratio, temperature and residence time on NO formation and applied to a furnace with co-axial diffusion flame burner.

• Nuclear Engineering and Technology
• /
• v.29 no.5
• /
• pp.406-416
• /
• 1997

A computational method is developed for predicting the steady-state temperature field in an LMR core. Detailed core-wide coolant temperature profiles are efficiently calculated using the simplified energy equation mixing model[1] and the subchannel analysis method. The $\theta$-method is employed for discretizing the energy equations in the axial direction. The interassembly coupling is achieved by interassembly gap flow. Cladding and fuel temperatures are calculated with the one-dimensional conduction model and temperature integrals of conductivities. The accuracy of the method is tested by performing several benchmark calculations for too LMR problems. The results indicate that the accuracy is comparable to the other methods based on ENERGY model. It is also shown that the implicit scheme for the axial discretization is more efficient than the explicit scheme.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.1-28
• /
• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Journal of computational fluids engineering
• /
• v.5 no.2
• /
• pp.47-54
• /
• 2000

A robust Navier-Stokes code has been developed to efficiently predict hypersonic flows in chemical nonequilibrium. The HLLE+ flux discretization scheme is used to improve accuracy and robustness of hypersonic flow analysis. An efficient LU approximate factorization method is also used to solve the flow equations and species continuity equations in fully coupled fashion to implicitly treat stiff source terms of chemical reactions. The HLLE+ scheme shows lower grid dependency for the wall heating rates than other schemes. The developed code has been used to compute chemical nonequilibrium air flow through expanding hypersonic nozzle and past two and three dimensional blunt-nosed bodies. The results are in good agreement with existing numerical and experimental results.

• Journal of the Korean Society of Industry Convergence
• /
• v.12 no.3
• /
• pp.149-155
• /
• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Steel and Composite Structures
• /
• v.19 no.5
• /
• pp.1237-1258
• /
• 2015

This paper proposes a simple inelastic analysis approach to efficiently map out the complete nonlinear post-collapse (strain-softening) response and the maximum load capacity of axially loaded concrete encased steel composite columns (stub and slender). The scheme simultaneously incorporates the influences of difficult instabilizing phenomena such as concrete confinement, initial geometric imperfection, geometric nonlinearity, buckling of reinforcement bars and local buckling of structural steel, on the overall behavior of the composite columns. The proposed numerical method adopts fiber element discretization and an iterative M${\ddot{u}}$ller's algorithm with an additional adaptive technique that robustly yields solution convergence. The accuracy of the proposed analysis scheme is validated through comparisons with various available experimental benchmarks. Finally, a parametric study of various key parameters on the overall behaviors of the composite columns is conducted.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.7 no.3
• /
• pp.396-405
• /
• 1995

Numerical calculations are carried out for the swirling turbulent flow in a pipe. Calculations are made for the flow with swirl parameter of 2.25 and the Reynolds number of 24,300. The turbulence closure models used in these calculations are two different types of Reynolds stress model, and the results are compared with those of $k-{\varepsilon}$ model and the experimental data. The finite volume method is used for the discretization, and the power-law scheme is employed as a numerical scheme. The SIMPLE algorithm is used for velocity-pressure correction. The computational results show that GL model gives the results better than those of SSG model in the predictions of velocity and stress components.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.11 no.6
• /
• pp.733-739
• /
• 1999

A modified low-Re $k-\varepsilon$ model is used for the calculation of drag-reducing turbulent flow by polymer injection in a pipe. With the viscoelastic model, molecular viscosity in the definition of turbulent viscosity is related to elongations viscosity of the solution to account for the effects of drag reduction. Finite volume method is used for the discretization, and power-law scheme is used as a numerical scheme. Computed dimensionless velocity profiles are in good agreements with the experimental data in case of low drag reductions. However, in case of high drag reductions, they deviate largely from the measurements in the central zone of the flow field.

• Proceedings of the SAREK Conference
• /
• 2006.06a
• /
• pp.116-121
• /
• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.3
• /
• pp.211-236
• /
• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.