Applicability of QSI Scheme to Advection-Diffusion Equations with Domain Decomposition Method

摘要

A fifth-order QSI (quintic spline interpolation) scheme was applied to advection-diffusion equations to obtain the steady and unsteady solutions with a domain decomposition method. The multiple subdomains, which are represented by curvilinear coordinates, include the overlapping grid points on the sides connected to the other sub-domains in the transformed space. The computational results obtained by the QSI scheme and some upwind difference methods were compared in terms of the numerical accuracy and computational time. The speedup was evaluated with the numbers of the grid points, N_c and N_m, which are used in the computations and message passings respectively, in addition to the processor number p. In particular, a partial implicit (PI) method was proposed to obtain steady solutions with the QSI scheme. As a result of the computations, validity of the QSI scheme and the related computational method was demonstrated.