Abstract
The approach of accelerating application with GPUs already delivers impressive computational performance compared to the traditional CPU. The hardware architecture of GPU is a significant departure from CPUs, hence the redesign and validation of the numerical algorithm are necessary. The spectral-finite-difference schemes usually used in the direction numerical simulation (DNS) for turbulent channel flows are studied here. In order to validate the numerical accuracy, the scalar diffusion equation is first solved with this scheme, and the results from GPU and CPU are validated with the analytical solution. The major computational kernels of the scheme are the fast Fourier transfer (FFT) and the linear equation solver, which are both implemented on GPU. The performance study of the scalar diffusion equation shows at least 20\(\times \) speedup. For 3D Navier-Stokes equation, the performance on a single Nvidia S2050 card shows 25 times speedup.
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Bell N, Garland M (2008) Efficient sparse matrix-vector multiplication on CUDA. NVIDIA Technical report NVR-2008-004, NVIDIA Corporation.
Bolz J, Farmer I, Grinspun E, Schröer P (2003) Sparse matrix solvers on the GPU: conjugate gradients and multigrid. In: SIGGRAPH’03: ACM SIGGRAPH, ACM, New York, NY, USA, pp 917–924.
Brandvik T, Pullan G (2008) Acceleration of a 3D Euler solver using commodity graphics hardware. In: 46th AIAA Aerospace sciences meeting and exhibit, Reno, Nevada, USA, AIAA-2008-607.
Cant S (2002) High-performance computing in computational fluid dynamics: progress and challenges. Phil Trans: Math Phys Eng Sci 360:1211–1225
Cortese TA, Balachandar S (1994) High performance spectral simulation of turbulent flows in massively parallel-machines with distributed memory. Technical report TAM Rep. 765, University of Illinois at Urbana-Champaign.
Crane K, Llamas I, Tariq S (2007) In: Real-Time simulation and rendering of 3D fluids, 3rd edn. Addison-Wesley, New York, pp 633–677
Elsen E, LeGresley P, Darve E (2008) Large calculation of the flow over a hypersonic vehicle using a GPU. J Comput Phys 227:10148–10161
Garg R, Ferziger JH, Monismith SG (1997) Hybrid spectral finite difference simulations of stratified turbulent flows on distributed memory architectures. Int J Numer Meth Fluids 24:1129–1158
Goodnight N, Woolley C, Lewin G, Luebke D, Humphreys G (2003) A multigrid solver for boundary value problems using programmable graphics hardware. In: HWWS’03: proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on graphics hardware, Eurographics Association, Aire-la-Ville, Switzerland pp 102–111.
Harris M, Baxter W, Scheuermann T, Lastra (2003) A Simulation of cloud dynamics on graphics hardware. In: HWWS’03: proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on graphics hardware, pp 92–101.
Khronos (2009) OpenCLWorking Group: The OpenCL specification. Specification.
Kim J, Moin P, Moser RD (1987) Turbulence statistics in fully developed channel flow at low reynolds number. J Fluid Mech 177:133–166
Kuznik F, Obrecht C, Rusaouen G, Roux JJ (2010) LBM based flow simulation using GPU computing processor. Comput Math Appl 59:2380–2392
Li W, Wei X, Kaufman A (2003) Implementing Lattice Boltzmann computation on graphics hardware. Vis Comput 9:444–456
Liu Y, Liu X, Wu E (2004) Real-time 3d fluid simulation on gpu with complex obstacles. In: 12th Pacific conference on computer graphics and applications, Seoul, South Korea pp 247–256.
Moin P, Kim J (1982) Numerical investigation of turbulent channel flow. J Fluid Mech 118:341–377
NVIDIA Corporation (2008) NVIDIA CUDA Compute Unified Device Architecture Programming Guide 2.0. (2008).
NVIDIA (2010) Cufft library. http://developer.nvidia.com/object/cuda-downloads.html (2010) CUDA Toolkit 3.2
Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2010) A new approach to the lattice boltzmann method for graphics processing units. Comput Math Appl 61(12):3628–3638
Stam J (1999) Stable fluids. In: SIGGRAPH 99 conference proceedings, Annual conference series, pp 121–128.
TOP 500 List. http://www.top500.org/lists/2011/06. Accessed April 2012
Zhao Y (2008) Lattice Boltzmann based pde solver on the GPU. Vis Comput 24:323–333
Acknowledgments
This work was supported by the National Science Foundation of China under Grant No. 10902063 and National Hi-tech Research and Development Program of China (863 Program) under Grant No. 2012AA01A308
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Xu, Y., Xu, L., Zhang, D.D., Yao, J.F. (2013). Investigation of Solving 3D Navier–Stokes Equations with Hybrid Spectral Scheme Using GPU. In: Yuen, D., Wang, L., Chi, X., Johnsson, L., Ge, W., Shi, Y. (eds) GPU Solutions to Multi-scale Problems in Science and Engineering. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16405-7_18
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DOI: https://doi.org/10.1007/978-3-642-16405-7_18
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