Research On Fission Matrix Acceleration Method And K-? Iteration Method

The eigenvalue calculations are important in the study of nuclear science and engi-neering.The k eigenvalue problem and a eigenvalue problem are common eigenvalue problems.The Monte Carlo(MC)criticality calculation always converges slowly in the system with a high dominance ratio close to unit.The acceleration method based on fission matrix has been proved the efficiency in the system with a high dominance ra-tio.To increase the efficiency of fission matrix acceleration method,a refined mesh is needed.But the fission matrix acceleration method with refined mesh needs more neu-trons to ensure the accuracy of fission matrix.In consideration of the total histories simulated,the increase of efficiency may be slight.The redistributing mesh method is a new attempt to accelerate the fission matrix acceleration method.When the mesh re-distributes in the process of iteration,the efficiency increases.The redistributing mesh method can accelerate the fission matrix acceleration method without a refined mesh.There are two common methods to solve the ? eigenvalue problem,the direct sim ulation method and the k-?iteration method.Although it is difficult to solve the sub-criticality problem with hydrogen,k-? iteration method is more efficient than di-rect simulation method in many cases.We analyze the k-? iteration method,and point out that the parameter in the k-? iteration method will affect the error estimation of? eigenvalue,but the real error estimation has no relationship with the parameter.If the parameter can not be given properly,the estimated error will deviate the real error estimation.The estimated error given by MCNP4C may deviate from the real error es-timation because of the improper parameter.A parameter selecting method called the average neutron fission lifetime method is proposed to make the estimated error and the real error estimation equal strictly in mathematics.These are all tested by the numerical experiment.