Advances in NS solver on GPU por M.Storti et.al. 
Advances in the Solution of NS Eqs. in GPGPU 
Hardware. Modelling Fluid ...
Advances in NS solver on GPU por M.Storti et.al. 
Scientific computing on GPUs 
 Graphics Processing Units (GPU’s) are spe...
Advances in NS solver on GPU por M.Storti et.al. 
Scientific computing on GPUs (cont.) 
 The difference between the GPUs 
...
Advances in NS solver on GPU por M.Storti et.al. 
Xeon Phi 
 In December 2012 Intel launched the Xeon Phi coprocessor card...
Advances in NS solver on GPU por M.Storti et.al. 
Xeon Phi (cont.) 
 Xeon Phi is an alien computer. It fits in a PCI Expre...
Advances in NS solver on GPU por M.Storti et.al. 
We want to use GPUs... for what? 
Aerodynamics of a racing car 
Aerodyna...
Advances in NS solver on GPU por M.Storti et.al. 
GPUs in HPC 
 Some HPC people are skeptical 
about the efficient computi...
Advances in NS solver on GPU por M.Storti et.al. 
Solution of incompressible Navier-Stokes flows on GPU 
 GPU’s are less e...
Advances in NS solver on GPU por M.Storti et.al. 
Fractional Step Method on structured grids with QUICK 
Proposed by Molem...
Advances in NS solver on GPU por M.Storti et.al. 
Solution of the Poisson with FFT 
 Solution of the Poisson equation is, ...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Sp...
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Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Spherical Buoy

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In this article we compare the results obtained with an implementation of the Finite Volume for structured meshes on GPGPUs with experimental results and also with a Finite Element code with boundary fitted strategy. The example is a fully submerged spherical buoy immersed in a cubic water recipient. The recipient undergoes an harmonic linear motion imposed with a shake table. The experiment is recorded with a high speed camera and the displacement of the buoy if obtained from the video with a MoCap (Motion Capture) algorithm. The amplitude and phase of the resulting motion allows to determine indirectly the added mass and drag of the sphere.

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Advances in the Solution of Navier-Stokes Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Spherical Buoy

  1. 1. Advances in NS solver on GPU por M.Storti et.al. Advances in the Solution of NS Eqs. in GPGPU Hardware. Modelling Fluid Structure Interaction for a Submerged Spherical Buoy by Mario Stortiab, Santiago Costarelliab, Luciano Garellia, Marcela Cruchagac, Ronald Ausensic, S. Idelsohnabde aCentro de Investigaci ´on de M´etodos Computacionales, CIMEC (CONICET-UNL) Santa Fe, Argentina, mario.storti@gmail.com, www.cimec.org.ar/mstorti bFacultad de Ingenier´ıa y Ciencias H´ıdricas. UN Litoral. Santa Fe, Argentina, fich.unl.edu.ar cDepto Ing. Mec´anica, Univ Santiago de Chile dInternational Center for Numerical Methods in Engineering (CIMNE) Technical University of Catalonia (UPC), www.cimne.com eInstituci ´o Catalana de Recerca i Estudis Avanc¸ats (ICREA), Barcelona, Spain, www.icrea.cat CIMEC-CONICET-UNL 1 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  2. 2. Advances in NS solver on GPU por M.Storti et.al. Scientific computing on GPUs Graphics Processing Units (GPU’s) are specialized hardware desgined to discharge computation from the CPU for intensive graphics applications. They have many cores (thread processors), currently the Tesla K40 (Kepler GK110) has 2880 cores at 745 Mhz (Builtin boost to 810, 875Mhz). The raw computing power is in the order of Teraflops (4.3 Tflops in SP and 1.43 Tflops in DP). Memory Bandwidth (GDDR5) 288 GB/sec. Memory size 12 GB. Cost USD 5,000. Low end version Geforce GTX Titan: USD 1000. CIMEC-CONICET-UNL 2 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  3. 3. Advances in NS solver on GPU por M.Storti et.al. Scientific computing on GPUs (cont.) The difference between the GPUs architecture and standard multicore processors is that GPUs have much more computing units (ALU’s (Arithmetic-Logic Unit) and SFU’s (Special Function Unit), but few control units. The programming model is SIMD (Single Instruction Multiple Data). GPUs compete with many-core processors (e.g. Intel’s Xeon Phi) Knights-Corner, Xeon-Phi 60 cores). if (COND) { BODY-TRUE; } else { BODY-FALSE; } CIMEC-CONICET-UNL 3 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  4. 4. Advances in NS solver on GPU por M.Storti et.al. Xeon Phi In December 2012 Intel launched the Xeon Phi coprocessor card: 3100 and 5110P. (2000 USD to 2600 USD). It has 60 cores with 22nm technology (clock speed 1GHz approx). “Supercomputer on a card” (SOC). Today limitation is that(with 22nm technology) is that 5e9 transistors can be put on a sinle chip. Today Xeon processors have typically 2.5e9 transistors. Xeon Phi has 60 cores equivalent to the original Pentium processor (40e6 transistors). CIMEC-CONICET-UNL 4 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  5. 5. Advances in NS solver on GPU por M.Storti et.al. Xeon Phi (cont.) Xeon Phi is an alien computer. It fits in a PCI Express X 16 slot, and has its own basic Linux system. You can SSH to the card and run x86-64 code. Another workflow is to run the code in the host and send intensive computing tasks to the card (e.g. solving a linear system). On January 2013 Texas Advanced Computing Center (TACC) added Xeon Phi’s to his Stampede supercomputer. Main CPUs are Xeon E5-2680. 128 nodes have Nvidia Kepler K20 GPUs. Estimated performance 7.6 Pflops. Tianhe-2 (China) the current fastes supercomputer (33.86 Pflops) includes also Xeon Phi coprocessors. Part of Intel’s Many Integrated Core (MIC) architecture. Previous codenames for the project: Larrabee, Knights Ferry, Knights-Corner.) CIMEC-CONICET-UNL 5 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  6. 6. Advances in NS solver on GPU por M.Storti et.al. We want to use GPUs... for what? Aerodynamics of a racing car Aerodynamics of an artillery projectile Flow patten in a harbour Dust particles in a coke processing facility Thermo fluid coupling Aerodynamics of a falling object Flutter at Ma=2.3 (launch video showall) CIMEC-CONICET-UNL 6 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  7. 7. Advances in NS solver on GPU por M.Storti et.al. GPUs in HPC Some HPC people are skeptical about the efficient computing power of GPUs for scientific applications. In many works speedup is referred to available CPU processors, which is not consistent. Delivered speedup w.r.t. mainstream x86 processors is often much lower than expected. Strict data parallelism is difficult to achieve on CFD applications. Unfortunately, this idea is reinforced by the fact that GPUs come from the videogame special effects industry, not with scientific computing. CIMEC-CONICET-UNL 7 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  8. 8. Advances in NS solver on GPU por M.Storti et.al. Solution of incompressible Navier-Stokes flows on GPU GPU’s are less efficient for algorithms that require access to the card’s (device) global memory. Shared memory is much faster but usually scarce (16K per thread block in the Tesla C1060) . The best algorithms are those that make computations for one cell requiring only information on that cell and their neighbors. These algorithms are classified as cellular automata (CA). Lattice-Boltzmann and explicit F?M (FDM/FVM/FEM) fall in this category. Structured meshes require less data to exchange between cells (e.g. neighbor indices are computed, no stored), and so, they require less shared memory. Also, very fast solvers like FFT-based (Fast Fourier Transform) or Geometric Multigrid are available . CIMEC-CONICET-UNL 8 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  9. 9. Advances in NS solver on GPU por M.Storti et.al. Fractional Step Method on structured grids with QUICK Proposed by Molemaker et.al. SCA’08: 2008 ACM SIGGRAPH, Low viscosity flow simulations for animation. Fractional Step Method (a.k.a. pressure segregation) u; v;w and continuity cells are staggered (MAC=Marker And Cell). QUICK advection scheme is used in the predictor stage. Poisson system is solved with IOP (Iterated Orthogonal Projection) (to be described later), on top of Geometric MultiGrid j+2 j+1 j Uij Pij Vij (ih,jh) i+1 i+2 x y i y-momentum cell x-momentum nodes y-momentum nodes x-momentum cell continuity nodes continuity cell CIMEC-CONICET-UNL 9 ((version cdcomp-enief2014-start-45-g8fb7450 Thu Oct 23 14:45:29 2014 -0300) (date Fri Oct 24 19:37:34 2014 -0300))
  10. 10. Advances in NS solver on GPU por M.Storti et.al. Solution of the Poisson with FFT Solution of the Poisson equation is, for large meshes, the more CPU consuming time stage in Fractional-Step like Navier-Stokes solvers. We have to solve a linear system Ax = b The Discrete Fourier Transform (DFT) is an orthogonal transformation ^x = Ox = t(x). The inverse transformation O

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