In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep-sea Munk speed profile. The research shows that, compared with the finite difference method, the Chebyshev spectral method has the advantages of a high computational accuracy and short computational time in underwater acoustic propagation.

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.

Summary The lattice Boltzmann method (LBM) is a widely used computational fluid dynamics method for flow problems with complex geometries and various boundary conditions. Large‐scale LBM simulations with increasing resolution and extending temporal range require massive https://en.wikipedia.org/wiki/High-performance_computing#High-performance computing (HPC) resources, thus motivating us to port it onto modern many‐core heterogeneous supercomputers like Tianhe‐2. Although many‐core accelerators such as graphics processing unit and Intel MIC have a dramatic advantage of floating‐point performance and power efficiency over CPUs, they also pose a tough challenge to parallelize and optimize computational fluid dynamics codes on large‐scale heterogeneous system. In this paper, we parallelize and optimize the open source 3D multi‐phase LBM code openlbmflow on the Intel Xeon Phi (MIC) accelerated Tianhe‐2 supercomputer using a hybrid and heterogeneous MPI+OpenMP+Offload+single instruction, mulitple data (SIMD) programming model. With cache blocking and SIMD‐friendly data structure transformation, we dramatically improve the SIMD and cache efficiency for the single‐thread performance on both CPU and Phi, achieving a speedup of 7.9X and 8.8X, respectively, compared with the baseline code. To collaborate CPUs and Phi processors efficiently, we propose a load‐balance scheme to distribute workloads among intra‐node two CPUs and three Phi processors and use an asynchronous model to overlap the collaborative computation and communication as far as possible. The collaborative approach with two CPUs and three Phi processors improves the performance by around 3.2X compared with the CPU‐only approach. Scalability tests show that openlbmflow can achieve a parallel efficiency of about 60% on 2048 nodes, with about 400K cores in total. To the best of our knowledge, this is the largest scale CPU‐MIC collaborative LBM simulation for 3D multi‐phase flow problems. Copyright © 2015 John Wiley & Sons, Ltd.

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The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve actual ocean acoustic fields using this model due to its application conditions and approximation error. Therefore, it is necessary to develop a direct solution method for the two-dimensional Helmholtz equation of ocean acoustic propagation without using simplified models. Here, two commonly used spectral methods, Chebyshev–Galerkin and Chebyshev–collocation, are used to correctly solve the two-dimensional Helmholtz model equation. Since Chebyshev–collocation does not require harsh boundary conditions for the equation, it is then used to solve ocean acoustic propagation. The numerical calculation results are compared with analytical solutions to verify the correctness of the method. Compared with the mature Kraken program, the Chebyshev–collocation method exhibits higher numerical calculation accuracy. Therefore, the Chebyshev–collocation method can be used to directly solve the representative two-dimensional ocean acoustic propagation equation. Because there are no model constraints, the Chebyshev–collocation method has a wide range of applications and provides results with high accuracy, which is of great significance in the calculation of realistic ocean sound fields.

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