SPECTRAL SOLUTION FOR TIME-DEPENDENT ONE-DIMENSIONAL TRANSPORT PROBLEM IN A SLAB

摘要

In this work we solve the time dependent radiative problem combining the spectral and LTSNrnmethods. For such the angular flux y(x,μ,t) is expanded in the time variable, in a truncatedrnLaguerre polynomial series :ψ(x,μ,t)=∑_(k=0)~L L_k(t)·ψ~k(x,μ)rnwhere L_k(t) are the Laguerre polynomials. Replacing this in the transport equation and takingrnmoments we come out with a set of steady-state problems which are solved by the LTS_N method.rnThe final solution is read as ψ_N(x)={∑_(k=1)~M e~(-s_kx)P_k}Aψ_N(0)+∑_(k=1)~M e~(-s_kx)P_k*Q_N(x)rnwhere P_k are the M matrizes of coefficients from the inversion of the Laplace transform, andrns_k are the eigenvalues of the square matrix sI + A .rnWe are going to present the numerical results for values of M up 89.rnWe complete the mathematical analysis of this approach by proving the convergence employingrntools of functional analysis.