Efficient parallel computing with a compact finite difference scheme

This paper proposes an efficient parallel computing approach based on a high-order accurate compact finite difference scheme in conjunction with a conventional domain decomposition method and MPI libraries. The proposed parallel computing approach consists of two major features: (a) a newly developed compact finite difference scheme with extended stencils containing halo points around subdomain boundaries, and (b) a predictor–corrector type implementation of a compact filter that effectively suppresses spurious errors from the subdomain boundaries. The current work employs three halo cells for the inter-node communication, based on which the coefficients of the new compact scheme at the subdomain boundaries are optimized to achieve as high level of resolution and accuracy as the interior compact scheme provides. Also, an optimal set of cut-off wavenumbers of the compact filter that minimizes spurious errors is suggested. It is shown that the level of errors from the proposed parallel calculations lies within the same order of magnitude of that from the single-domain serial calculations. The overall accuracy and linear stability of the new parallel compact differencing-filtering system are confirmed by grid convergence tests and eigenvalue analyses. The proposed approach shows a substantial improvement with respect to existing methods available.