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For computational fluid dynamics (CFD) applications with a large number of grid points/cells, parallel computing is a common efficient strategy to reduce the computational time. How to achieve the best performance in the modern supercomputer system, especially with heterogeneous computing resources such as hybrid CPU+GPU, or a CPU + Intel Xeon Phi (MIC) co-processors, is still a great challenge. An in-house parallel CFD code capable of simulating three dimensional structured grid applications is developed and tested in this study. Several methods of parallelization, performance optimization and code tuning both in the CPU-only homogeneous system and in the heterogeneous system are proposed based on identifying potential parallelism of applications, balancing the work load among all kinds of computing devices, tuning the multi-thread code toward better performance in intra-machine node with hundreds of CPU/MIC cores, and optimizing the communication among inter-nodes, inter-cores, and between CPUs and MICs. Some benchmark cases from model and/or industrial CFD applications are tested on the Tianhe-1A and Tianhe-2 supercomputer to evaluate the performance. Among these CFD cases, the maximum number of grid cells reached 780 billion. The tuned solver successfully scales up to half of the entire Tianhe-2 supercomputer system with over 1.376 million of heterogeneous cores. The test results and performance analysis are discussed in detail.

A three-dimensional (3D) finite difference (FD) model with formal fourth-order accuracy has been developed for the ocean acoustic Helmholtz equation (HE), which can be used to address arbitrary bathymetry and provide more accurate benchmark solutions for other 3D underwater acoustic approximate models. The derivatives in the acoustic HE are numerically discretized based on regular grids, and the perfectly matched layer is introduced to absorb unphysical reflections from the boundaries where Sommerfeld radiation conditions are deployed. The system of linear equations is solved using a parallel matrix-free geometric multigrid preconditioned biconjugate gradient stabilized iteration method, and the code (named COACH) is run on the Tianhe-2 supercomputer in China. Four 3D topographic benchmark acoustic cases—a wedge waveguide, Gaussian canyon, conical seamount, and corrugated seabed—are simulated to test the present FD model, and the maximum number of grid points reaches 33.15 × 109 in the wedge waveguide case, running in parallel with 988 central processing unit cores. Furthermore, the accuracy and generality of the present model have been verified by solution comparisons with other available 3D acoustic propagation models, and the two-dimensional and 3D transmission loss contours are presented to facilitate the distinguishing among the acoustic field features of these cases.

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