Error bounds for some characteristic methods in an exceptional case

Abstract

Abstract New characteristic methods for the solution of the x,y geometry discrete ordinates neutron transport equation have recently been introduced. Five polynomials, without any continuity requirement are defined on each mesh cell. A polynomial of order k is used to approximate the angular flux inside the cell, while polynomial approximations of order l are used along the cell edges. Error bounds for a pure absorber calculation by this Ckl characsteristic method are given here for l lower or equal to 1 and for the simplest case. In this case, that we shall call the exceptional case, a uniform spatial mesh grid with rectangles of length △x and height △y is used, and the angular quadrature directions ω = (μ, ν) verify the condition (the characteristic lines are the diagonals of the cells). It is proved that, in a discrete L2 norm, thre Ckl method has a convergene rate equal to Min (k+2, 2l+1) for regular data and solution, and equal to Min for more realistic situations. We also provide some numerical resu...