PWS: an efficient code system for solving space-independent nuclear reactor dynamics

Aboanber, Ahmed E.; Hamada, Yasser Mohamed

doi:10.1016/s0306-4549(02)00034-8

Cited by 44 publications

(18 citation statements)

References 13 publications

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“…The TS solution has had a long history and was one of the first methods to be considered (see [Vi67] and [Vi71]). The method has been modified many times thereafter (see, for example, [Mi77], [Le95], [AbHa02], and [Ke65]). We will again consider the TS solution, but now with convergence acceleration.…”

Section: Nuclear Reactor Kineticsmentioning

confidence: 99%

Integral Methods in Science and Engineering

2013

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Section: Nuclear Reactor Kineticsmentioning

confidence: 99%

Integral Methods in Science and Engineering

2013

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“…Among the methods that have been discussed are Power Series Solutions (PWS) (Aboanber, 2002, Sathiyasheela 2009), CORE (Quintero-Leyva, 2008), and PCA (Kinard and Allen, 2003). Each of these methods is highly accurate, but they vary widely in complexity of implementation.…”

Section: Introductionmentioning

confidence: 99%

A highly accurate technique for the solution of the non-linear point kinetics equations

Picca

Furfaro

Ganapol

2013

Annals of Nuclear Energy

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The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step gives results that are comparable to those obtained using other popular yet more complicated methods. The algorithm developed using a Taylor series expansion is simple, completely transparent, and highly accurate. The procedure is tested using a variety of initial conditions and input data, including step reactivity, ramp reactivity, sinusoidal, pulse, and zigzag reactivity. These results are compared to those obtained using other methods.

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“…Furthermore, a very small step size has to be adopted for stability due to the problem of stiffness in the differential equations when applying a general numerical method. Many numerical methods have been proposed in the literature, such as stiffness confinement method [22] and power series solution [23][24][25][26]. Several other creative schemes have been implemented as well as da Nóbrega [27], Lawrence and Doring [28], and Aboanber and Nahla [29] use a Padé approximation to the solution of the point kinetics equations.…”

Section: Introductionmentioning

confidence: 99%

Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics

Aboanber

2013

International Journal of Nuclear Energy

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The base of reactor kinetics dynamic systems is a set of coupled stiff ordinary differential equations known as the point reactor kinetics equations. These equations which express the time dependence of the neutron density and the decay of the delayed neutron precursors within a reactor are first order nonlinear and essentially describe the change in neutron density within the reactor due to a change in reactivity. Outstanding the particular structure of the point kinetic matrix, a semianalytical inversion is performed and generalized for each elementary step resulting eventually in substantial time saving. Also, the factorization techniques based on using temporarily the complex plane with the analytical inversion is applied. The theory is of general validity and involves no approximations. In addition, the stability of rational function approximations is discussed and applied to the solution of the point kinetics equations of nuclear reactor with different types of reactivity. From the results of various benchmark tests with different types of reactivity insertions, the developed generalized Padé approximation (GPA) method shows high accuracy, high efficiency, and stable character of the solution.

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PWS: an efficient code system for solving space-independent nuclear reactor dynamics

Cited by 44 publications

References 13 publications

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering

A highly accurate technique for the solution of the non-linear point kinetics equations

Generalized and Stability Rational Functions for Dynamic Systems of Reactor Kinetics

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