The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.

(Maciej Matyka, Zbigniew Koza, Łukasz Mirosław: “Wall Orientation and Shear Stress in the Lattice Boltzmann Model”, Preprint, 2012. [arXiv])

We study the use of a GPU for the numerical approximation of the curvature dependent flows of graphs – the mean-curvature flow and the Willmore flow. Both problems are often applied in image processing where fast solvers are required. We approximate these problems using the complementary finite volume method combined with the method of lines. We obtain a system of ordinary differential equations which we solve by the Runge–Kutta–Merson solver. It is a robust solver with an automatic choice of the integration time step. We implement this solver on CPU but also on GPU using the CUDA toolkit.  We demonstrate that the mean-curvature flow can be successfully approximated in single precision arithmetic with the speed-up almost 17 on the Nvidia GeForce GTX 280 card compared to Intel Core 2 Quad CPU. On the same card, we obtain the speed-up 7 in double precision arithmetic which is necessary for the fourth order problem – the Willmore flow of graphs. Both speed-ups were achieved without affecting the accuracy of the approximation. The article is structured in such way that the reader interested only in the implementation of the Runge–Kutta–Merson solver on the GPU can skip the sections containing the mathematical formulation of the problems.

(Oberhuber T., Suzuki A., Žabka V.: “The CUDA implementation of the method of lines for the curvature dependent flows”, Kybernetika 47(2):251–272, 2011. [PDF])

• One of the fastest Sparse Matrix Vector Multiplication worldwide.
• Faster Conjugate Gradient and BiConjugate Gradient solvers.
• State-of-the-art CMRS format for storing sparse matrices. The format requires less memory than CRS or HYB (from CUSPARSE and CUSP).
• Faster acceleration in OpenFOAM (Computational Fluid Dynamics).

More information is available at http://speed-it.vratis.com.

• PCG – Preconditioned conjugate gradient solver for symmetric matrices (e.g., p)
• PBiCG – Preconditioned biconjugate gradient solver for asymmetric matrices (e.g., Ux, k)

ofgpu also has support for the OpenFOAM preconditioners:

• no
• diagonal

For more details see “GPU Linear Solver Library for OpenFOAM”. OpenFOAM is a registered trademark of OpenCFD and is unaffiliated with Symscape.

In this paper, we present the design of Power Flow algorithm that has enhanced performance on the Graphics Processing Unit (GPU) using Compute Unified Device Architecture (CUDA). This work investigates the performance of optimized CPU versions of Newton-Raphson (Polar form) and Gauss-Jacobi power flow algorithms, highlights the approach used to reduce the computation time by performing these studies on massively parallel GPU cores. Simulations results demonstrate the significant acceleration of the GPU version compared to its CPU variant, thus reducing processing time making them suitable for real-time online dispatching purposes.

(Singh, J. and Aruni, I.: “Accelerating Power Flow studies on Graphics Processing Unit”, Proceedings of the Annual IEEE India Conference 2010 (INDICON), pp 1-5, Dec. 2010. [DOI])

We present a computational method of coupling average interpolating wavelets with high-order finite volume schemes and its implementation on heterogeneous computer architectures for the simulation of multiphase compressible flows. The method is implemented to take advantage of the parallel computing capabilities of emerging heterogeneous multicore/multi-GPU architectures. A highly efficient parallel implementation is achieved by introducing the concept of wavelet blocks, exploiting the task-based parallelism for CPU cores, and by managing asynchronously an array of GPUs by means of OpenCL. We investigate the comparative accuracy of the GPU and CPU based simulations and analyze their discrepancy for two-dimensional simulations of shock-bubble interaction and Richtmeyer–Meshkov instability. The results indicate that the accuracy of the GPU/CPU heterogeneous solver is competitive with the one that uses exclusively the CPU cores. We report the performance improvements by employing up to 12 cores and 6 GPUs compared to the single-core execution. For the simulation of the shock-bubble interaction at Mach 3 with two million grid points, we observe a 100-fold speedup for the heterogeneous part and an overall speedup of 34.

(Rossinelli D., Hejazialhosseini B., Spampinato D., Koumoutsakos P.: “Multicore/Multi-GPU Accelerated Simulations of Multiphase Compressible Flows Using Wavelet Adapted Grids”, SIAM Journal of Scientific Computing 33:512-540, 2011 [DOI])

ACUSim vortex shedding

From a recent press release:

ACUSIM Software, Inc., a leader in computational fluid dynamics (CFD) technology and solutions, today announced the immediate availability of AcuSolve™ 1.8, the latest version of ACUSIM’s leading general-purpose, finite-element based CFD solver. ACUSIM will demonstrate AcuSolve 1.8 during two free webinars, taking place at 9:30 a.m. – 10:30 a.m. ET and 6:30 p.m. – 7:30 p.m. ET, on Oct. 26, 2010, at http://www.acusim.com/html/events.html.

Used by designers and research engineers with all levels of expertise, AcuSolve is highly differentiated by its accelerated speed, robustness, accuracy and multiphysics/multidisciplinary capabilities. Contributing to its robustness is the product’s Galerkin/Least-Square (GLS) finite element formulation and novel iterative linear equation solver for the fully coupled equation system. The combination of these two powerful technologies provides a highly stable and efficient solver, capable of handling unstructured meshes with tight boundary layers automatically generated from complex industrial geometries.

“ACUSIM’s products are known for their advanced solver technology including Fluid-Structure Interaction solutions,” said Dr. Farzin Shakib, founder and CEO of ACUSIM Software. “While continuously adding to its core technology, the latest version of AcuSolve is concentrated on providing customers with ease of use and CAE automation to solve mission critical problems in a more efficient and timely fashion.”

AcuSolve 1.8 users will experience improvements and new features in the core technology and pre-processing and post-processing phases. These enhancements include:

• Core Technology:
  • Enriched simulation capabilities of ACUSIM’s leading Fluid-Structure Interaction (FSI) technology with added interface to MD Nastran
  • Extended Arbitrary Lagrangian Eulerian (ALE) Formulation to handle compressible flows with large density variation and mesh motion
  • Anisotropic thermal conductivity
  • Improved Free Surface Technology with the addition of multi-iterative coupling based nonlinear update solver
  • New Algebraic Multi-Grid (AMG) Technology for faster flow convergence and optimized linear solver performance
  • Support for GPU acceleration based on NVIDIA CUDA 3.0 technology

• Pre-processing:
  • Much improvement in meshing such as region of influence and anisotropic meshing and edge control
  • CAE Automation and Customization with improved Template Driven and Customization Driven Automation and batch oriented processing
  • Interface to electromechanical simulation software JMAG to perform full thermal flow analysis on electro-magnetic devices
  • Easier deployment with existing corporate Cloud Computing Clusters and Dassault Simulia SLM systems
  • Embedded CAD geometry generator

• Post-processing:
  • New AcuSolve/Paraview co-process visualization
  • Full batch-oriented report generation capability including text, pagination, equations, tables, 2D plots, full 3D visualization and animation
  • New flexible input structure for AcuSolve’s particle tracer, with the ability to add user evolution equations

New features:

• Multi-GPU communication library
• Multi-GPU versions of Multigrid solver, Incompressible Navier-Stokes solver, and more
• NetCDF support now optional
• Support for Fermi/CUDA 3.0
• Numerous bug fixes and enhancements

Get it here: http://code.google.com/p/opencurrent/downloads/list