Second-order Time Evolution Scheme for Time-dependent Neutron Transport Equation

In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

• Zhenying Hong
• Guangwei Yuan
• Xuedong Fu
• Shulin Yang

• Exponential method
• diamond difference
• modified time discrete scheme
• second-order time evolution scheme.

[1] E.E.Lewis, W.F.Miller, Computational methods of neutron transport(M).
La Grange Park. Amermos Nuclear Societ(1993).
[2] T.Nkaoua, R.Sentis, A new time discretization for the radiative transfer
equations: analysis and comparison with the classical discretization(J).
SIAM J.NUMER.ANAL., 30,733-748(1993).
[3] R.H.Szilard, G.C.Pomraning, Numerical transport and diffusion methods
in radiative transfer(J). Nucl.Sci.Eng., 112,256-269(1992).
[4] G.G.McClarren, A quasi-linear implementation of high-resolution time
integration for PN the equations(J). Nucl.Sci.Eng., 159, 330-337(2008).
[5] J.E.Morel., Wareing.T.A., A linear-discontinuous spatial differencing
scheme for Sn radiative transfer calculations(J). J.Comp.Phys., 128, 445-
462(1996).
[6] Gordon L.Olson, Second-order time evolution of PN equations for
radiation transport(J). J.Comput.Phys., 228, 3072-3083(2009).
[7] Gordon L.Olson, Efficient solution of multi-dimensional flux-limited
nonequilibrium radiation diffusion coupled to material conduction
with second-order time discretization(J). J.Comput.Phys., 226, 1181-
1195(2007).
[8] K.D.Lathrop, Spatial differencing the transport equation: positivity vs.
accuracy(J). J.Comp.Phys., 4, 475-498(1969).
[9] Zhengying Hong, Guangwei Yuan, Xudong Fu, Oscillation
of numerical for time-dependent particle transport equation(J).
Prog.Nucl.Energy.,52315-320(2010).
[10] Zhengying Hong, Guangwei Yuan, Xudong Fu, Shulin Yangm, Modified
time discrete scheme for time-dependent neutron transport equation(J).
Chinese Nuclear Power Engineering(accepted).
[11] Zhengying Hong, Guangwei Yuan, Xudong Fu, Methods of determining
iterative initial value for time-dependent neutron transport equation(J).
Journal On Numerical Methods and Computer Applications.,29,4:302-
312(2008)