On the Analytical Solution of the Multi-Group Neutron Diffusion Kinetic Equation in One-Dimensional Cartesian Geometry by an Integral Transform Technique
The Generalized Integral Transform Technique, henceforth named GITT approach, is a well established methodology to solve analytically linear differential equations for a broad class of problems in the area of physics and engineering. By analytical we mean that no approximation is done along the derivation of the solution, except for the truncation of the solution series in numerical computations. The main idea of this approach relies on the construction of a pair of transformations from the Laplacian adjoint terms appearing in the differential equation to be solved. This fact allows us to write the solution as a series expansion in terms of the orthogonal eigenfunctions obtained from the solution of an auxiliary Sturm–Liouville problem constructed from the adjoint terms.
KeywordsThermal Neutron Fast Neutron Liouville Problem Matrix Differential Equation Coordinate Research Project
Unable to display preview. Download preview PDF.
- [Abd06]Ait-Abderrahim, H., Stanculescu, A.: IAEA Coordinate Research Project on Analytical and Experimental Benchmark Analyses of Accelerator Driven Systems. Proceedings of ANS Topical Meeting on Reactor Physics, Paper C074 (2006). Google Scholar
- [Bod10]Bodmann, B.E.J., de Vilhena, M.T., Ferreira, L.S., Bardaji, J.B.: An analytical solver for the multi-group two-dimensional neutron-diffusion equation by integral transform techniques. Il Nuovo Cimento, 33 C, n. 1, 63–70 (2010). Google Scholar
- [Cot98]Cotta, R.M. (Org.): The Integral Transform Method in Thermal and Fluids Science and Engineering, Begell House, Inc., New York (1998). Google Scholar
- [Dul07]Dulla, S., Ravetto, P., Picca, P., Tomatis, D.: Analytical benchmarks for the kinetics of accelerator-driven systems. Joint International Topical Meeting on Mathematics & Computation and Supercomputing in Nuclear Applications, (2007). Google Scholar
- [Mai07]Maiorino, J.R.: The Participation of IPEN in the AIEA Coordinate Research Projects on Accelerator Driven Systems (ADS). International Nuclear Atlantic Conference – INAC, (2007). Google Scholar
- [Mol78]Moler, C., Van Loan, C.: Nineteen dubious ways of computing the exponential of a matrix. SIAM Review, 801–836 (1978). Google Scholar
- [Oli07]Oliveira, F.L., Maiorino, J.R., Santos, R.S.: The analytical benchmark solution of spatial diffusion kinetics in source driven systems for homogeneous media. International Nuclear Atlantic Conference – INAC, (2007). Google Scholar
- [Seg99]Segatto, C.F., Vilhena, M.T., Gomes, M.G.: The one dimensional LTSn solution in a slab with high degree of quadrature. Annals of Nuclear Energy, 26, 925–934 (1999). Google Scholar
- [Seg08]Segatto, C.F., Vilhena, M.T., Marona, D.V.: The LTSn solution of the transport equation for one-dimensional Cartesian geometry with c=1. Kerntechnik, 73, 57–60 (2008). Google Scholar