Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation (Q1299333)

Two operator splitting algorithms for the two-dimensional advection-diffusion equation are presented. Both algorithms are second-order accurate adaptations of the first-order accurate splitting scheme introduced by \textit{F. M. Holly jun.} and \textit{A. Preissmann} [Accurate calculation of transport in two dimensions, Proc. ASCJ J. Hyd. Div. 103, 1259-1277 (1977)]. As most of the previously reported operator splitting algorithms are first-order accurate, due to splitting errors, the method of constructing second-order accurate splitting algorithms is discussed and an error analysis is presented. The numerical analyses performed in this paper show that both operator splitting algorithms are second-order accurate, in time and space, and have similar mass conservation properties.