Efficient Implementation of Nonlinear Compact Schemes on Massively Parallel Platforms

Weighted nonlinear compact schemes are ideal for simulating compressible, turbulent flows because of their nonoscillatory nature and high spectral resolution. However, they require the solution to banded systems of equations at each time-integration step or stage. We focus on tridiagonal compact schemes in this paper. We propose an efficient implementation of such schemes on massively parallel computing platforms through an iterative substructuring algorithm to solve the tridiagonal system of equations. The key features of our implementation are that it does not introduce any parallelization-based approximations or errors and it involves minimal neighbor-toneighbor communications. We demonstrate the performance and scalability of our approach on the IBM Blue Gene/Q platform and show that the compact schemes are efficient and have performance comparable to that of standard noncompact finite-difference methods on large numbers of processors (∼ 500, 000) and small subdomain sizes (4 points per dimension per processor).