We examine the super compact symmetric finite difference scheme (SCSFD) and compare it with traditional difference methods and compact difference methods. The result shows high efficiency of SCSFD. According to the characteristics of the algorithm, a parallel algorithm named block pipelined method for three-dimensional compressible Navier-Stokes equations using SCSFD is designed and its parallel performance is analysed. Numerical experiments are carried out.

We present a parallel bisection mesh refinement algorithm based on ALBERT (Adaptive multi-Level finite element toolbox using Bisection refinement and Error control by Residual Techniques). The goal is to develop a parallel adaptive finite element code suitable for distributed memory parallel computers or PC clusters. An overview on the basic strategy for the parallelization of ALBERT is given. Issues on the parallel mesh refinement are addressed. A modified mesh refinement algorithm, which can be implemented efficiently on distributed memory parallel computers, is proposed and its properties are discussed. Numerical experiments with parallel bisection mesh refinement algorithm are shown.

Based on the high accuracy compact difference scheme and the alternating group explicit (AGE) iterative method which has obvious property of parallelism,an AGE iterative method with the fourth-order compact scheme is established for the steady convection-diffusion equation.Numerical solutions are obtained for the model problem of natural convection in a square cavity with large Rayleigh number of physical interest and small Prandtl numbers attempted.Some results of the present are compared with the referenced paper.