Practical CFD Simulations on Programmable Graphics Hardware using SMAC†

Abstract

The explosive growth in integration technology and the parallel nature of rasterization-based graphics APIs (Application Programming Interface) changed the panorama of consumer-level graphics: today, GPUs (Graphics Processing Units) are cheap, fast and ubiquitous. We show how to harness the computational power of GPUs and solve the incompressible Navier-Stokes fluid equations significantly faster (more than one order of magnitude in average) than on CPU solvers of comparable cost. While past approaches typically used Stam's implicit solver, we use a variation of SMAC (Simplified Marker and Cell). SMAC is widely used in engineering applications, where experimental reproducibility is essential. Thus, we show that the GPU is a viable and affordable processor for scientific applications. Our solver works with general rectangular domains (possibly with obstacles), implements a variety of boundary conditions and incorporates energy transport through the traditional Boussinesq approximation. Finally, we discuss the implications of our solver in light of future GPU features, and possible extensions such as three-dimensional domains and free-boundary problems.

Multidisciplinary Simulation Acceleration using Multiple Shared-Memory Graphical Processing Units

“…Scheidegger et al were able to show that NVIDIA GPUs based on the NV35 and NV40 architectures were well suited for CFD 5 simulations using the SMAC (Simplified Marker and Cell) method. With sufficiently dense grids, they were able to achieve speedup factors as high as 21 12 . Similarly, Hagen et al achieved speedups as high as 20 using NVIDIA GeForce GPUs.…”

“…For example, if a threedimensional array x(i,j,n) were created in Fortran, the data in the first ('i') column would be ordered 12 sequentially in system memory. That is, the data stored at x(2,1,1) would be directly adjacent in memory to the data stored at x(1,1,1).…”

“…Research has shown that GPUs can reliably produce an order of magnitude speedup, when measured against comparable high performance CPUs, for a wide range of scientific applications [5][6][7][8][9][10][11][12][13][14][15] . Bolz et al…”

Running Unstructured Grid Based CFD Solvers on Modern Graphics Hardware

“…In fact, just prior to its first release, Owens et al 9 comprehensively surveyed the field of general-purpose computation on graphics hardware (GPGPU), which included a number of primarily structured grid based solvers, such as those of Harris, 10 Scheidegger et al, 11 and Hagen et al 12 However, the architecture has changed substantially and many of the limitations of GPGPU via traditional graphics APIs such as OpenGL are no longer an issue.…”

Unsteady Turbulent Simulations on a Cluster of Graphics Processors

“…Many of these researchers implement fluid simulations, however, most are limited to the 2D incompressible Navier-Stokes equations using pressure projection methods [5][6][7][8][9] , which are interesting from a performance and simulation point of view, but use simplified numerics which lack the proper accuracy required for engineering design applications. Furthermore, negelecting the effects of compressibility leads to much simpler formulations which are not applicable to transonic and supersonic flows of interest.…”