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The point kinetic equations are the system of a couple stiff ordinary differential equations. Many studies have focused on the development of more advanced and efficient methods of solving the equations, such as the high order Taylor polynomials method, the Haar wavelet operational method, the fractional point-neutron kinetic model method, the basis function method, the homotopy analysis method, and other methods. Most of these methods are successful in some specific problems, but still have, more or less, disadvantages. For example, the accuracy of the Haar wavelet operational method is limited by the collocation points, and it needs more computing time for a high precision. Aiming at the requirements that some numerical calculation results must have the higher precision and only the positive error in the nuclear reactor safety engineering and ship reactor for the maneuverability, in this paper we try to look for a new numerical method to satisfy that the calculation value is slightly higher than the real value when the actual curve is upward convex or downward concave, and the error is not greater than that by the Euler and improved Euler method. The new method is so-called the curvature weight (CW) method, which is based on the curvature circle method and considers the contributions of two curvatures at the interval step point to the average curvature inside the interval step. Using the decoupling method to remove the stiffness of equations and the instantaneous jump approximation to derive the neutron differential equations, the first and second derivative of neutron density are obtained. Then the CW method is used to solve the point reactor neutron kinetic equations, and thus obtaining the numerical solution. Compared with the results by the Euler and improved Euler method, the numerical calculation results by the CW method are always higher than the real value, and the calculation accuracy and speed are improved significantly. When this new method is used to solve the point reactor neutron differential equations with the step and linear reactivity inserted into the subcritical reactor, the numerical results which satisfy the requirements of positive calculation error and high precision can be obtained quickly. After improving the calculation step length, the precision reduction by the CW method is significantly lower than that by the Euler and improved Euler method. So the CW method can greatly shorten the total computing time, and it is also effective for most of differential equation systems.
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Keywords:
- curvature weight method /
- neutron kinetics /
- point-reactor /
- subcritical reactor
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[2] Huang Z Q 2007 Kinetics Base of Nuclear Reactor (Beijing: Peaking University Press) p174 (in Chinese) [黄祖洽 2007 核反应堆动力学基础 (北京: 北京大学出版社) 第174页]
[3] Zhu Q, Shang X L, Chen W Z 2012 Acta Phys. Sin. 61 070201 (in Chinese) [朱倩, 商学利, 陈文振 2012 物理学报 61 070201]
[4] Cai Z S, Cai Z M, Chen L S 2001 Nucl. Power Engng. 22 390 (in Chinese) [蔡章生, 蔡志明, 陈力生 2001 核动力工程 22 390]
[5] Cai Z S 2005 Nuclear Power Reactor Neutron Dynamics (Bejing: National Industry Press) pp171-177 (in Chinese) [蔡章生 2005 核动力反应堆中子动力学 (北京: 国防工业出版社) 第171177页]
[6] Li H F, Chen W Z, Zhu Q, Luo L 2008 Atom. Energy Sci. Technol. 42(sl) 162 (in Chinese) [黎浩峰, 陈文振, 朱倩, 罗磊 2008 原子能科学技术 42(sl) 162]
[7] Vyawahare V A, Nataraj P S V 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1840
[8] Nowak T K, Duzinkiewica K, Riotrowski P 2014 Ann. Nucl. Energ. 73 317
[9] Chakraverty S, Tapaswini S 2014 Chin. Phys. B 23 120202
[10] Ray S S, Patra A 2013 Ann. Nucl. Energ. 54 154
[11] Patra A, Ray S S 2014 Ann. Nucl. Energ. 68 112
[12] Patra A, Ray S S 2014 Ann. Nucl. Energ. 73 408
[13] Chen W Z, Xiao H G, Li H F, Chen L 2015 Ann. Nucl. Energ. 75 353
[14] Tasic B, Mattheij R M 2004 Appl. Math. Comput. 156 633
[15] Butcher J C 2000 J. Comput. Appl. Math. 125 1
[16] Wu X Y 1998 Comput. Math. Appl. 35 59
[17] Wu X, Xia J 2000 Comput. Math. Appl. 39 247
[18] Snchez J 1989 Nucl. Sci. Eng. 103 94
[19] Zhang F, Chen W Z, Gui X W 2008 Ann. Nucl. Energ. 35 746
[20] Li H F, Chen W Z, Luo L, Zhu Q 2009 Ann. Nucl. Energ. 36 427
[21] Li H F, Chen W Z, Zhang F, Chen Z Y 2010 Prog. Nucl. Energ. 52 321
[22] Li H F, Chen W Z, Zhang F, Shang X L 2010 Acta Phys. Sin. 59 2375 (in Chinese) [黎浩峰, 陈文振, 张帆, 商学利 2010 物理学报 59 2375]
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[1] L Z Q, Zhang L M, Wang Y S 2014 Chin. Phys. B 23 120203
[2] Huang Z Q 2007 Kinetics Base of Nuclear Reactor (Beijing: Peaking University Press) p174 (in Chinese) [黄祖洽 2007 核反应堆动力学基础 (北京: 北京大学出版社) 第174页]
[3] Zhu Q, Shang X L, Chen W Z 2012 Acta Phys. Sin. 61 070201 (in Chinese) [朱倩, 商学利, 陈文振 2012 物理学报 61 070201]
[4] Cai Z S, Cai Z M, Chen L S 2001 Nucl. Power Engng. 22 390 (in Chinese) [蔡章生, 蔡志明, 陈力生 2001 核动力工程 22 390]
[5] Cai Z S 2005 Nuclear Power Reactor Neutron Dynamics (Bejing: National Industry Press) pp171-177 (in Chinese) [蔡章生 2005 核动力反应堆中子动力学 (北京: 国防工业出版社) 第171177页]
[6] Li H F, Chen W Z, Zhu Q, Luo L 2008 Atom. Energy Sci. Technol. 42(sl) 162 (in Chinese) [黎浩峰, 陈文振, 朱倩, 罗磊 2008 原子能科学技术 42(sl) 162]
[7] Vyawahare V A, Nataraj P S V 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1840
[8] Nowak T K, Duzinkiewica K, Riotrowski P 2014 Ann. Nucl. Energ. 73 317
[9] Chakraverty S, Tapaswini S 2014 Chin. Phys. B 23 120202
[10] Ray S S, Patra A 2013 Ann. Nucl. Energ. 54 154
[11] Patra A, Ray S S 2014 Ann. Nucl. Energ. 68 112
[12] Patra A, Ray S S 2014 Ann. Nucl. Energ. 73 408
[13] Chen W Z, Xiao H G, Li H F, Chen L 2015 Ann. Nucl. Energ. 75 353
[14] Tasic B, Mattheij R M 2004 Appl. Math. Comput. 156 633
[15] Butcher J C 2000 J. Comput. Appl. Math. 125 1
[16] Wu X Y 1998 Comput. Math. Appl. 35 59
[17] Wu X, Xia J 2000 Comput. Math. Appl. 39 247
[18] Snchez J 1989 Nucl. Sci. Eng. 103 94
[19] Zhang F, Chen W Z, Gui X W 2008 Ann. Nucl. Energ. 35 746
[20] Li H F, Chen W Z, Luo L, Zhu Q 2009 Ann. Nucl. Energ. 36 427
[21] Li H F, Chen W Z, Zhang F, Chen Z Y 2010 Prog. Nucl. Energ. 52 321
[22] Li H F, Chen W Z, Zhang F, Shang X L 2010 Acta Phys. Sin. 59 2375 (in Chinese) [黎浩峰, 陈文振, 张帆, 商学利 2010 物理学报 59 2375]
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