• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.19-34
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• 2016

In this paper, we present a split least-squares characteristic mixed finite element method(MFEM) to get the approximate solutions of the convection dominated Sobolev equations. First, to manage both convection term and time derivative term efficiently, we apply a least-squares characteristic MFEM to get the system of equations in the primal unknown and the flux unknown. Then, we obtain a split least-squares characteristic MFEM to convert the coupled system in two unknowns derived from the least-squares characteristic MFEM into two uncoupled systems in the unknowns. We theoretically prove that the approximations constructed by the split least-squares characteristic MFEM converge with the optimal order in L² and H¹ normed spaces for the primal unknown and with the optimal order in L² normed space for the flux unknown. And we provide some numerical results to confirm the validity of our theoretical results.

• East Asian mathematical journal
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• v.35 no.5
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• pp.569-587
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• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.

• East Asian mathematical journal
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• v.38 no.3
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• pp.293-319
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• 2022

In this paper, we introduce a higher order split least-squares characteristic mixed element scheme for Sobolev equations. First, we use a characteristic mixed element method to manipulate both convection term and time derivative term efficiently and obtain the system of equations in the primal unknown and the flux unknown. Second, we define a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We establish the convergence results for the primal unknown and the flux unknown with the second order in a time increment.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2396-2401
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• 2007

Freon CHF experiments are carried out to investigate the CHF enhancements by mixing vane shapes of spacer grids in nuclear fuel assembly. The experiments were performed for a wide range mass flux, 50$\sim}$3000 kg/$m^2s$. Three kinds of spacer grids in 5${\times}$5 rod bundles are tested: no mixing vane grids, hybrid mixing vane grids, and split mixing vane grids. The CHF performances are compared along with the data belong to the PWR operating conditions based on a water equivalence through a fluid-to-fluid modeling method. The average of the data in this range is 16.4% for 37 data of hybrid vane grid and 12.5% for 24 data of split vane. In the lower mass flux, however, the split vane grid shows slightly higher performance than the hybrid vane grid.

• Journal of computational fluids engineering
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• v.4 no.2
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• pp.57-66
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• 1999

Numerical Analysis has been done for the supersonic off-design jet flow due to the pressure difference between the jet and the ambient fluid. The difference of pressure generates an oblique shock or an expansion wave at the nozzle exit. The waves reflect repeatedly on the center axis and the sonic surface in the shear layer. The pressure difference is resolved across these reflected waves. In this paper, the axi-symmetric Navier-Stokes equation has been used with the κ-ε turbulence model. The second order TVD scheme with flux limiters, based on the flux vector split with the smooth eigenvalue split, has been used to capture internal shocks and other discontinuities. Numerical calculations have been done to analyze the off-design jet flow due to the pressure difference. The variation of pressure along the flow axis is compared with an experimental result and other numerical result. The characteristics of the interaction between the shock cell and the turbulence mixing layer have been analyzed.

• Journal of Electrical Engineering and Technology
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• v.10 no.1
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• pp.251-260
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• 2015

The main purpose of this paper is to describe a DTC (direct torque control) method for four-switch brushless dc motor (BLDCM) drive. In the method, a novel voltage space vector modulation scheme, an optimal switching table, and a flux observation method are proposed. Eight voltage vectors are summarized, which are selected to control BLDCM in SVPWM pattern, and an optimal switching table is proposed to improve the torque distortion caused by midpoint current of the split capacitors. Unlike conventional flux observers, this observer does not require speed adaptation and is not susceptible to speed estimation errors, especially, at low speed. Global asymptotic stability of the flux observer is guaranteed by the Lyapunov stability analysis. DC-offset effects are mitigated by introducing a PI component in the observer gains. This method alleviates the undesired current and torque distortion which is caused by uncontrollable phase. The correctness and feasibility of the method are proved by simulation and experimental results.

• Nuclear Engineering and Technology
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• v.34 no.4
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• pp.382-395
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• 2002

An experimental study on transient critical heat flux (CHF) under flow coastdown has been performed for the water flow in a non-uniformly heated vertical annulus under low flow and a wide range of pressure conditions. The objectives of this study are to systematically investigate the effect of the flow transient on the CHF and to compare the transient CHF with steady-state CHF The transient CHF experiments have been performed for three kinds of flow transient modes based on the coastdown data of a nuclear power plant reactor coolant pump. At the same inlet subcooling, system pressure and heat flux, the effect of the initial mass flux on the critical mass flux can be negligible. However, the effect of the initial mass flux on the time-to- CHF becomes large as the heat flux decreases. The critical mass flux has the largest value for slow flow reduction rate. There is a pressure effect on the ratio of the transient CHF data to steady-state CHF data. Except under low system pressure conditions, the flow transient CHF was revealed to be conservative compared with the steady-state CHF data. Bowling CHF correlation and thermal hydraulic system code MARS show promising results for the prediction of CHF occurrence .

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.156-157
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• 2003

A simple method is proposed to split the flux vector of the Euler equations by introducing two artificial wave speeds. The direction of wave propagation can be adjusted by these two wave speeds. This idea greatly simplifies the upwinding, and leads to a new family of upwind schemes. Numerical flux function for multi-dimensional Euler equations is formulated for any grid system, structured or unstructured. A remarkable simplicity of the scheme is that it successfully achieves one-sided approximation for all waves without recourse to any matrix operation. Moreover, its accuracy is comparable with the exact Riemann solver. For 1-D Euler equations, the scheme actually surpasses the exact solver in avoiding expansion shocks without any additional entropy fix. The scheme can exactly resolve stationary contact discontinuities, and it is also freed of the carbuncle problem in multi­dimensional computations.

• Journal of Power Electronics
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• v.15 no.4
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• pp.974-986
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• 2015

A novel inverter fault-tolerant control scheme is proposed to drive brushless DC motor. A fault-tolerant inverter and its three fault-tolerant schemes (i.e., phase A fault-tolerant, phase B fault-tolerant, and phase C fault-tolerant) are analyzed. Eight voltage vectors are summarized and a voltage vector selection table is used in the control scheme to improve the midpoint current of the split capacitors. A stator flux observer is proposed. The observer can improve flux estimation, which does not require any speed adaptation mechanism and is immune to speed estimation error. Global stability of the flux observer is guaranteed by the Lyapunov stability analysis. A novel stator resistance estimator is incorporated into the sensorless drive to compensate for the effects of stator resistance variation. DC offset effects are mitigated by introducing an integral component in the observer gains. Finally, a control system based on the control scheme is established. Simulation and experiment results show that the method is correct and feasible.

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.