• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.131-136
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• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1391-1402
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• 2021

The aim of this work is to prepare a neutron noise calculator based on the second order of average current nodal expansion method (ACNEM). Generally, nodal methods have the ability to fulfill the neutronic analysis with adequate precision using coarse meshes as large as a fuel assembly size. But, for the zeroth order of ACNEM, the accuracy of neutronic simulations may not be sufficient when coarse meshes are employed in the reactor core modeling. In this work, the capability of second order ACNEM is extended for solving the neutron diffusion equation in the frequency domain using coarse meshes. For this purpose, two problems are modeled and checked including a slab reactor and 2D BIBLIS PWR. For validating of results, a semi-analytical solution is utilized for 1D test case, and for 2D problem, the results of both forward and adjoint neutron noise calculations are exploited. Numerical results indicate that by increasing the order of method, the errors of frequency dependent coarse mesh solutions are considerably decreased in comparison to the reference. Accordingly, the accuracy of second order ACNEM can be acceptable for the neutron noise calculations by using coarse meshes in the nuclear reactor core.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1-4
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• 1996

It is difficult that a non-translational motion in a block is estimated by the block matching algorithm (BMA). In this paper, a nodal-displacement-based deformation model is used for this reason. This model assumes that a selected number of control nodes move freely in a block and that displacement of any interior point can be interpolated from nodal displacements. As a special case with a single node this model is equivalent to a translational model. And this model can represent more complex deformation using more nodes. We used an iterative gradient based search algorithm to estimate nodal displacement. Each iteration involves the solution of a simple linear equation. This method is called the deformable block matching algorithm (DBMA).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1123-1131
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• 2005

In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.387-398
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• 1998

We investigate the existence of radial nodal solutions of the elliptic equation $\Delta$u ＋ h($\mid$x$\mid$)f(u) = 0, in annular domains. It is proved that for each integer k $\geq$ 1, there exist at least one radially symmetric solution which has exactly k nodes.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05a
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• pp.137-141
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• 1996

A new general high order consistent nodal method for solving the 3-D multigroup neutron kinetic equations in (x-y-z) geometry has been derived by expending the flux in a multiple polynomial series for the space variables by without the quadratic fit approximations of the transverse leakage and for the time variable and using a weighted-integral technique. The derived equation set is consistent mathematically, and therefore, we can expect very accurate solutions and less computing time since we can use coarse meshes in time variable as well as in spatial variables and the solution would converge exactly in fine mesh limit.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.1
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• pp.160-166
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• 2005

In this paper, the combined system equation of motion, which can analyze the dynamic interaction between pantograph and catenary system, is derived by adopting absolute nodal coordinates and rigid body coordinates. The analysis results are compared with real experiment data from test running of Korean high-speed train (HSR 350x). In addition, a computation method for the dynamic stress of contact wire is presented using the derived system equation of motion. This method might be good example and significant in that the structural and multibody dynamics model can be unified into one numerical system.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.345-368
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• 2004

A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decoupling the nodal and side bases from the internal bases. Its implementation consists of solving a global problem on the wire-basket and a series of local problems defined on a single element. Moreover, the condition number of the preconditioned system is shown to be of order $O((1＋ln/p)^{7})$. This technique can be applied to discretization with triangular elements and with general basis functions.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.649-654
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• 2004

A physically simple but mathematically cumbrous problem of rotating heavy chain with one fixed top point is studied. Nonlinear equation of its two-dimensional shapes of relative equilibrium is obtained and solved numerically. A linear case of small displacements is analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions is studied with the help of simulation using the absolute nodal coordinate formulation (ANCF). The equilibriums are found instable, and the reason of instability is explained using a variational principle.