求解中子输运方程的粗网格再平衡方法
|
摘要
针对已知中子输运方程的标量通量P1近似值和网格边界通量模型情况下,我们提出了一种求解中子输运方程新的粗网格再平衡方法.方法将再平衡系统的稀疏矩阵变成对角占优矩阵,同时矩阵的逆是非负的.
In the current work, the authors develop a technique to make the coefficient matrix of rebalance system, which is used in coarse mesh rebalance method, to be diagonally dominant. This technique is based on the P1 approximation of scalar flux and the mode of net currents at the cell boundaries when the angular flux is not less than zero. Moreover, the inversion of the matrix is nonnegative.
In the current work, the authors develop a technique to make the coefficient matrix of rebalance system, which is used in coarse mesh rebalance method, to be diagonally dominant. This technique is based on the P1 approximation of scalar flux and the mode of net currents at the cell boundaries when the angular flux is not less than zero. Moreover, the inversion of the matrix is nonnegative.
引文
[1] Adams M L. Fast iterative methods for discrete-ordinates particle transport calculations, Prog.Nucl. Energ, 2002, 40(1):3-159.
[2] Yamamoto A. Generalized coarse mesh rebalance method for acceleration of neutron transport calculations[], Nucl Sci Engy, 2005, 151:274-282.
[3] Yamamoto A, Kitamura Y, Ushio T, and Sugimura N. Convergence improvement of coarse mesh rebalance method for neutron transport calculations[J]. J Nucl Sci Tech, 2012, 41(8):781-789.
[4] Cho N Z, Park C J. A comparison of coarse mesh rebalance and coarse mesh finite difference accelerations for the neutron transport calculations, Nuclear mathematical and computational sciences:A century in Review, Gatlinburg, Tennessee, April, 2003:6-11.
[5] Lathrop K D. Spatial differencing of the transport equation:Positivity vs accuracy[J]. J Comput Phys, 1969, 4:217-237.
[6] Maginot P G, Morel J E, Ragusa J C. A non-negatvie momentpreserving spatial discretization scheme for the linearized Boltzmann transport equation in 1-D and 2-D Cartesian geometries[J]. J Comput Phys, 2012, 231:6801-6826.
[7] Yuan D M, Cheng J, Shu C W. High order positivity-preserving disconitinous Galerkin methods for radiative transfer equations[J]. SIAM J Sci Comput, 2016, 38(5):2987-3019.
[8] Varga R S. Matrix iterative analysis(second edition, in English), Science Press, Beijing, China, 2006.
[2] Yamamoto A. Generalized coarse mesh rebalance method for acceleration of neutron transport calculations[], Nucl Sci Engy, 2005, 151:274-282.
[3] Yamamoto A, Kitamura Y, Ushio T, and Sugimura N. Convergence improvement of coarse mesh rebalance method for neutron transport calculations[J]. J Nucl Sci Tech, 2012, 41(8):781-789.
[4] Cho N Z, Park C J. A comparison of coarse mesh rebalance and coarse mesh finite difference accelerations for the neutron transport calculations, Nuclear mathematical and computational sciences:A century in Review, Gatlinburg, Tennessee, April, 2003:6-11.
[5] Lathrop K D. Spatial differencing of the transport equation:Positivity vs accuracy[J]. J Comput Phys, 1969, 4:217-237.
[6] Maginot P G, Morel J E, Ragusa J C. A non-negatvie momentpreserving spatial discretization scheme for the linearized Boltzmann transport equation in 1-D and 2-D Cartesian geometries[J]. J Comput Phys, 2012, 231:6801-6826.
[7] Yuan D M, Cheng J, Shu C W. High order positivity-preserving disconitinous Galerkin methods for radiative transfer equations[J]. SIAM J Sci Comput, 2016, 38(5):2987-3019.
[8] Varga R S. Matrix iterative analysis(second edition, in English), Science Press, Beijing, China, 2006.