High-order space–time parallel computing of the Navier–Stokes equations

Abstract

Space–time parallel methods can leverage modern parallel computing architectures to further accelerate numerical simulations where parallelizing only in space limits concurrency. In this paper, we develop a high-order space–time parallel computing method for solving the Navier–Stokes equations. The method is based on revisionist integral deferred correction (RIDC) algorithm proposed by Christlieb, Macdonald and Ong [SIAM J. Sci. Comput., 32 (2010), pp. 818-835]. This parallel-in-time algorithm yields high-order accurate results within a wall-clock time comparable to that of a forward or backward Euler simulation. We extend the RIDC algorithm to a space–time parallel method and apply the method to a compressible fluid solver using the message passing interface (MPI) framework. The global communicator is split into space and time communicators to manage parallel computing in spatial and temporal domains, respectively. Accuracy tests show that the method is high-order accurate. Numerical results encompassing both smooth flows and flows with discontinuities demonstrate that the proposed method can accelerate the computation robustly. Additionally, a three-dimensional space–time parallel computation of flow around a sphere is performed. The results indicate that RIDC has the potential to be used in the field of computational fluid dynamics.