High-Order CFD Methods Research Articles

Flow field and particle dispersion in a naturally ventilated model building: Application of large eddy simulation based on parallel lattice Boltzmann method

Flow field analysis and pollutant particles tracking in a natural ventilation flow are computationally intensive due to the coupled outdoor and indoor airflow, as well as the existence of different turbulence scales, and large numbers of particles. As a breakthrough approach, an explicit and parallel algorithm based on lattice Boltzmann method (LBM) solver is developed to simulate transient particulate flow indoor and outdoor of a model building. Since flow analysis in natural ventilation requires high-order CFD methods, large eddy simulation (LES) by the wall-adapting local eddy-viscosity (WALE) sub-grid scales model is employed. Also, one-step collision for reduction of memory usage, domain decomposition method for parallel processing of both flow and particles, and Lagrangian tracking for following particles are implemented into the developed algorithm. Investigation of grid independency shows that medium lattice resolution provides an average mean deviation equal to 18% and 34% for horizontal and vertical centerline of model building, respectively. In addition, when compared to finite volume method (FVM), LBM requires 2.7 times higher lattice resolution to achieve acceptable accuracy. However, it approximately speeds simulation duration up to 3 times. Moreover, 100 seconds of parallel particle tracking lasts almost 800 minutes on a simple desktop.

Designing CFD methods for bandwidth—A physical approach

A hoped-for outcome from high-order CFD methods, in addition to achieving accurate solutions on fine grids, is to achieve useful answers on coarse grids. In this paper we note that this outcome is by no means automatic, and consider how the different quests of accuracy and bandwidth may be achieved. Although accuracy is exclusively a low-frequency property and so amenable to Taylor series analysis, bandwidth is concerned with higher frequencies and may not be approachable by this route. It is argued that an important aspect should be the physically correct flow of information, especially for hyperbolic problems, and that this is strongly influenced by the choice of computational stencil. This is confirmed by applying von Neumann analysis to the linear advection equation, giving a strong preference to odd-order fully discrete schemes using upwind-biased stencils. However, it is pointed out that these schemes do not always generalize to higher dimensions, and a method is shown that achieves very accurate directionality even on unstructured grids. This is accomplished by taking information from the exact solution to the multidimensional IVP for acoustics.

High-Order Overset Flux Reconstruction Method for Dynamic Moving Grids

Overset meshes have a unique advantage in handling moving boundary problems as remeshing is often unnecessary. Recently, overset Cartesian and strand meshes were used successfully to compute complex flow over rotorcraft. Although it is quite straightforward to deploy a high-order finite difference method on the Cartesian mesh, the near-body solver for the strand mesh is often limited to second-order accuracy. In the present study, a high-order flux reconstruction solver, hpMusic, is developed on both the near-body and background grids, and it is extended to handle moving boundary problems. Accuracy studies are carried out, and the designed order of accuracy is obtained for both inviscid and viscous flows. The method is then tested for a benchmark dynamic airfoil problem from the 4th International Workshop on High-Order CFD Methods. Mesh and order-convergent results are obtained and compared with those from other groups. Finally flow over a hovering rotor is simulated to compare with experimental data. In this case, the present high-order solver is capable of generating and propagating tip vortices with high resolution. Good agreement is achieved with experimental data in tip vortex core size, location, and the swirl velocity at third-order accuracy.

Efficiency benchmarking of seventh-order tri-diagonal weighted compact nonlinear scheme on curvilinear mesh

ABSTRACTEfficiency improvements of high-order weighted compact nonlinear scheme (WCNS) are verified using a series of benchmark cases, proposed at the International Workshop on High-Order CFD Methods. A seventh-order tri-diagonal compact one of WCNSs (WCNS-E8T7), constructed in recent years, is investigated as a basic scheme, and compared to a typical fifth-order explicit WCNS (WCNS-E6E5) and a traditional second-order TVD scheme MUSCL. Among these tests, a symmetrical conservative metric method (SCMM) is adopted to ensure the accuracy and robustness of WCNSs when solving cases in the curvilinear coordinates. The computational efficiency of schemes is evaluated based on a non-dimensional cost in achieving the same level of accuracy. Related results show that WCNS-E8T7 has a better performance than WCNS-E6E5 with the same interpolation stencils. Moreover, the opinion that high-order methods can obtain higher computational efficiency than second-order methods is demonstrated on the cases ranging from academic problems to real-life computations.

Efficiency Benchmarking of an Energy Stable High-Order Finite Difference Discretization

In this paper, results are presented for a number of benchmark cases, proposed at the 2nd International Workshop on High-Order CFD Methods in Cologne, Germany, in 2013. A robust high-order-accurate finite difference method was used that was developed during the last 10–15 years. The robustness stems from the fact that the entire numerical procedure, including various kinds of boundary conditions, can be proven stable. This paper outlines the methodology, and it summarizes results presented at the workshop along with some more data and tests.

OpenMP performance with an Euler code on an Intel based personal computer

Personal computers of the past were limited to running computational fluid dynamics codes in serial mode. With the advent of multicore technology and suitable compilers, personal computers nowadays can execute codes in a parallel fashion similar to that of supercomputers and cluster computer systems. This article investigated what performance can be achieved when executing an aerodynamic code on an Intel quad core based personal computer with an OpenMP compiler in a Windows environment. The code solved the Euler equations to find the flowfield around a NACA0012 aerofoil on an O-type boundary fitted structured grid system. A speedup of up to 350% was obtainable in double precision accuracy. The reduced computation time means that, for small scale problems, more accurate Euler codes can replace commonly used transonic small disturbance codes. For larger problems, this information serves as a reference for developers of hybrid MPI/OpenMP algorithms for cluster computer systems. References Advanced Micro Devices (AMD), AMD FireStream 9170: Industry's First GPU with Double-Precision Floating Point, 2007, http://ati.amd.com/products/streamprocessor/specs.html Allmaras, S. R., Venkatakrishnan, V., and Johnson, F. T., Farfield Boundary Conditions for 2-D Airfoils, AIAA Paper 2005-4711, AIAA, 2005. Bailey, D., Barszcz, E., Barton, J., Browning, D., Carter, R., Dagum, L., Fatoohi, R., Fineberg, S., Frederickson, P., Lasinski, T., Schreiber, R., Simon, H., Venkatakrishnan, V., and Weeratunga, S., The NAS Parallel Benchmarks, National Aeronautics and Space Administration (NASA), Contractor Report 203186, USA, 1994, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970014936_1997021577.pdf Dong, S., and Karniadakis, G. E., Dual-Level Parallelism for High-Order CFD Methods, Parallel Computing, 30, Jan. 2004, pp. 1--20. Hirsch, C., Numerical Computation of Internal and External Flows (Volume 2): Computational Methods for Inviscid and Viscous Flows, John Wiley and Sons, Great Britain, 1992. Hoffmann, K. A., Computational Fluid Dynamics for Engineers, Engineering Educational System, Texas, USA, 1989. Intel, Tera-scale Computing Research Program, c.2007, http://www.intel.com/research/platform/terascale/ Jin, H., Frumkin, M., and Yan, J., The OpenMP Implementation of NAS Parallel Benchmarks and its Performance, National Aeronautics and Space Administration (NASA), Technical Report NAS-99-011, Moffett Field, USA, 1999. Liu, Y., and Vinokur, M., Nonequilibrium Flow Computations 1: An Analysis of Numerical Formulations of Conservation Laws, National Aeronautics and Space Administration (NASA), Contractor Report 177489, California, USA, 1988, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19880021000_1988021000.pdf Lock, R. C., Test Cases for Numerical Methods in Two-Dimensional Transonic Flows, Advisory Group for Aerospace Research and Development (AGARD), Report Number 575, 1970. Ly, E., Improved Approximate Factorisation Algorithm for the Steady Subsonic and Transonic Flow over an Aircraft Wing, Proceedings of the 21st Congress of the International Council of the Aeronautical Sciences (ICAS98), ICAS and AIAA, Melbourne, Australia, 1998, Paper A98-31699. Ly, E., and Gear, J. A., Time-Linearized Transonic Computations Including Shock Wave Motion Effects, Journal of Aircraft, 39, 6, Nov/Dec. 2002, pp. 964--972. Ly, E., and Nakamichi, J., Time-Linearised Transonic Computations Including Entropy, Vorticity and Shock Wave Motion Effects, The Aeronautical Journal, Nov. 2003, pp. 687--695. Ly, E., and Norrison, D., Automatic Elliptic Grid Generation by an Approximate Factorisation Algorithm, ANZIAM Journal, 48 (CTAC2006), pp. C188--C202, July 2007, http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/48. Ly, E., and Norrison, D., Generating Elliptic Grids in Three Dimensions by a Method of False Transients, ANZIAM Journal, 49 (EMAC2007), pp. C170--C183, Nov. 2007, http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/313. Nvidia, The Era of the Personal Supercomputer, 2007, http://www.nvidia.com/content/events/siggraph_2007/supercomputing.html Pope, S. B., A Perspective on Turbulence Modeling, Modeling Complex Turbulent Flows, Kluwer Academic Publishers, The Netherlands, 1999. Pulliam, T., Kutler, P., and Rossow, V., Harvard Lomax: His Quiet Legacy to Computational Fluid Dynamics, 14th AIAA Computational Fluid Dynamics Conference, Norfolk, VA, 28 June-1 July, 1999, http://people.nas.nasa.gov/ pulliam/mypapers/lomax_la.ps Steger, J. L., and Warming, R. F., Flux Vector Splitting of the Inviscid Gasdynamic Equations with Application to Finite Difference Methods, National Aeronautics and Space Administration (NASA) Technical Memorandum 78605, California, USA, 1979, http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790020779_1979020779.pdf Thompson, J. R., Warsi, Z. U. A., and Mastin, C. W., Numerical Grid Generation: Foundations and Applications, Elsevier Science Publishing Co. Inc., New York, USA, 1985. Van Leer, B., Flux-Vector Splitting for the Euler Equations, Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen, West Germany, 1982.

Multilevel Parallelization Models in CFD

*† We present two multilevel parallel models based on MPI/MPI (MPI denoting Message Passing Interface) and MPI/OpenMP (OpenMP denoting Open Multi-Processing) for highorder CFD methods and compare their performances. These models are implemented within the spectral/hp element framework to take advantage of the hierarchical structures arising from deterministic and stochastic CFD computations. For MPI/MPI, we employ MPI process groups to decompose the computations into different levels. For MPI/OpenMP, we take a Single-Program-Multiple-Data (SPMD) style approach to OpenMP shared memory parallelism that significantly reduces the OpenMP synchronizations. These models demonstrate a good scalability with respect to the problem size and a good speedup for fixed problem sizes. With identical configurations, the MPI/MPI parallel model is observed to be generally more efficient. The advantage of these multilevel approaches lies in that they reduce the number of processes participating in each communication and the latency overhead, and thus enable the applications to scale to a large number of processors more efficiently. The models have been applied to the direct simulation of turbulent flows past a circular cylinder at Reynolds number Re=10,000.

Dual-level parallelism for high-order CFD methods

A hybrid two-level parallel paradigm with MPI/OpenMP is presented in the context of high-order methods and implemented in the spectral/ hp element framework to take advantage of the hierarchical structures arising from deterministic and stochastic CFD problems. We take a coarse grain approach to OpenMP shared-memory parallelization and employ a workload-splitting scheme that reduces the OpenMP synchronizations to the minimum. The hybrid algorithm shows good scalability with respect to both the problem size and the number of processors for a fixed problem size. For the same number of processors, the hybrid model with 2 OpenMP threads per MPI process is observed to perform better than pure MPI and pure OpenMP on the SGI Origin 2000 and the Intel IA64 Cluster, while the pure MPI model performs the best on the IBM SP3 and on the Compaq Alpha Cluster. A key new result is that the use of threads facilitates effectively p-refinement, which is crucial to adaptive discretization using high-order methods.