High-Order Spectral Difference: Verification and Acceleration using GPU Computing
High-Order Spectral Difference: Verification and Acceleration using GPU Computing
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高阶谱差：使用 GPU 计算进行验证和加速
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Visbal
中科院分区：
文献类型：
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作者：
B. Zimmerman;Z. Wang;M. Visbal
使用统一计算设备架构 (CUDA) 的图形处理单元 (GPU) 开发了高阶光谱差 (SD) 方法。它通过 RungeKutta 时间积分求解非结构化六面体网格上的三维 Navier-Stokes 方程。该方法非常有效，因为运算以一维方式完成，并且方程以微分形式求解，消除了显式的表面和体积积分计算。此外，解和通量重建是在每个单元本地完成的，从而增加了实现的并行化。由于这种效率，GPU计算的应用很有吸引力。本文介绍了使用 GPU CUDA 计算实现 SD 方法，并介绍了各向同性涡流传播和 Couette 流的精度研究，验证了求解器在数值敏感的气动声学问题上的高阶精度，并将所开发的求解器和高阶有限差分求解器与第一届高阶 CFD 方法国际研讨会上提出的案例进行了比较。最后，将 GPU 求解器与类似的中央处理单元 (CPU) 求解器进行比较，其中显示速度提高了 20-40 倍。
A high-order spectral difference (SD) method has been developed with graphics processing units (GPUs) using compute unified device architecture (CUDA). It solves the three-dimensional Navier-Stokes equations on unstructured hexahedral grids with RungeKutta time integration. The method is efficient since operations are completed in a onedimensional fashion and the equations are solved in differential form, removing explicit surface and volume integral calculations. Additionally, solution and flux reconstructions are completed locally per cell, increasing the parallelization of the implementation. Due to this efficiency, the application of GPU computing is appealing. This paper presents the SD method implementation with GPU CUDA computing and presents accuracy studies with isotropic vortex propagation and Couette flow, verifies the high-order accuracy of the solver with a numerical sensitive aero-acoustic problem, and compares the developed solver and a high-order finite difference solver with a case presented in the 1st International Workshop on High-Order CFD Methods. Finally, the GPU solver is compared to a similar central processing unit (CPU) solver, where speed-ups ranging from 20-40x faster are illustrated.