Abstract In this article, the high-order upwinding combined compact difference scheme developed in a three-point grid stencil is applied to solve the incompressible Navier-Stokes (NS) and energy equations in three dimensions. The time integrator with symplectic property is employed to approximate the temporal derivative term in inviscid Euler equation so as to numerically retain the embedded Hamiltions and Casimir to get long-time accurate solutions. For the sake of computational efficiency in solving the three-dimensional NS equations, all the calculations will be accelerated using the hybrid CUDA and OpenAcc GPU programing models. The parallel speedup performance compared to the multicore of an Intel Xeon E5-2690V5 CPU is reported.

中文翻译：

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用于模拟 GPU 中三维流动和传热问题的高阶组合紧致有限差分方案的加速

摘要 在本文中，应用在三点网格模板中开发的高阶迎风组合紧致差分格式来求解不可压缩的 Navier-Stokes (NS) 和三维能量方程。采用具有辛性质的时间积分器对无粘欧拉方程中的时间导数项进行近似，从而在数值上保留嵌入的Hamiltions和Casimir，从而得到长时间的精确解。为了求解三维 NS 方程的计算效率，所有计算都将使用混合 CUDA 和 OpenAcc GPU 编程模型进行加速。报告了与 Intel Xeon E5-2690V5 CPU 的多核相比的并行加速性能。