×

A parallel direct cut algorithm for high-order overset methods with application to a spinning golf ball. (English) Zbl 1416.76103

Summary: Overset methods are commonly employed to enable the effective simulation of problems involving complex geometries and moving objects such as rotorcraft. This paper presents a novel overset domain connectivity algorithm based upon the direct cut approach suitable for use with GPU-accelerated solvers on high-order curved grids. In contrast to previous methods it is capable of exploiting the highly data-parallel nature of modern accelerators. Further, the approach is also substantially more efficient at handling the curved grids which arise within the context of high-order methods. An implementation of this new algorithm is presented and combined with a high-order fluid dynamics code. The algorithm is validated against several benchmark problems, including flow over a spinning golf ball at a Reynolds number of 150,000.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation

Software:

Gmsh; TIOGA; GiMMiK; Helios; HOPR; PyFR

References:

[1] Meakin, R. L., Composite overset structured grids, (Thompson, J. F.; Soni, B. K.; Weatherill, N. P., Handbook of Grid Generation (1999), CRC Press), Ch. 11 · Zbl 0980.65500
[2] Wissink, A., An overset dual-mesh solver for computational fluid dynamics, (7th International Conference on Computational Fluid Dynamics. 7th International Conference on Computational Fluid Dynamics, ICCFD7 (2012))
[3] Pulliam, T. H., High order accurate finite-difference methods: as seen in overflow, (20th AIAA Computational Fluid Dynamics Conference (2011))
[4] Buning, P. G.; Pulliam, T. H., Near-body grid adaption for overset grids, (46th AIAA Fluid Dynamics Conference (2016))
[5] Wissink, A., Helios solver developments including strand meshes, oral presentation, (11th Symposium on Overset Composite Grids and Solution Technology (2012))
[6] Nastase, C.; Mavriplis, D.; Sitaraman, J., An overset unstructured mesh discontinuous Galerkin approach for aerodynamic problems, (49th AIAA Aerospace Sciences Meeting (2011))
[7] Vincent, P.; Witherden, F.; Vermeire, B.; Park, J. S.; Iyer, A., Towards green aviation with python at petascale, (Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’16 (2016), IEEE Press: IEEE Press Piscataway, NJ, USA)
[8] Vermeire, B. C.; Witherden, F. D.; Vincent, P. E., On the utility of GPU accelerated high-order methods for unsteady flow simulations: a comparison with industry-standard tools, J. Comput. Phys., 333, 497-521 (2017)
[9] W.H. Reed, T.R. Hill, Triangular Mesh Methods for the Neutron Transport Equation, Los Alamos Scientific Laboratory Technical Report LA-UR-73-379.; W.H. Reed, T.R. Hill, Triangular Mesh Methods for the Neutron Transport Equation, Los Alamos Scientific Laboratory Technical Report LA-UR-73-379.
[10] Kopriva, D. A.; Kolias, J. H., A conservative staggered-grid Chebyshev multidomain method for compressible flows, J. Comput. Phys., 125, 244-261 (1996) · Zbl 0847.76069
[11] Sun, Y.; Wang, Z. J.; Liu, Y., High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids, Commun. Comput. Phys., 2, 310-333 (2007) · Zbl 1164.76360
[12] Huynh, H. T., A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, (47th AIAA Aerospace Sciences Meeting (2009))
[13] Hesthaven, J. S.; Warburton, T., Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications (2008), Springer-Verlag: Springer-Verlag New York · Zbl 1134.65068
[14] Romero, J.; Witherden, F.; Jameson, A., A direct flux reconstruction scheme for advection-diffusion problems on triangular grids, J. Sci. Comput., 73, 1115-1144 (2017) · Zbl 1381.65084
[15] Galbraith, M. C., A Discontinuous Galerkin Overset Solver (2013), University of Cincinnati, Ph.D. Thesis
[16] Brazell, M. J.; Sitaraman, J.; Mavriplis, D., An overset mesh approach for 3d mixed element high order discretizations, (53rd AIAA Aerospace Sciences Meeting (2015)) · Zbl 1351.76050
[17] Brazell, M. J.; Kirby, A. C.; Mavriplis, D. J., A high-order discontinuous-Galerkin octree-based AMR solver for overset simulations, (23rd AIAA Computational Fluid Dynamics Conference (2017))
[18] Galbraith, M. C.; Benek, J. A.; Orkwis, P. D.; Turner, M. G., A discontinuous Galerkin chimera scheme, Comput. Fluids, 98, 27-53 (2014) · Zbl 1391.76327
[19] Crabill, J.; Jameson, A.; Sitaraman, J., A high-order overset method on moving and deforming grids, (AIAA Modeling and Simulation Technologies Conference (2016)), AIAA2016-3225
[20] Duan, Z.; Wang, Z. J., A high order FR/CPR method for overset strand and cartesian meshes and moving boundaries, (23rd AIAA Computational Fluid Dynamics Conference (2017))
[21] Kirby, A. C.; Brazell, M. J.; Yang, Z.; Roy, R.; Ahrabi, B. R.; Mavriplis, D. J.; Stoellinger, M. K.; Sitaraman, J., Wind farm simulations using an overset hp-adaptive approach with blade-resolved turbine models, (23rd AIAA Computational Fluid Dynamics Conference (2017))
[22] Chandar, D. D.; Sitaraman, J.; Mavriplis, D., GPU parallelization of an unstructured overset grid incompressible Navier-Stokes solver for moving bodies, (50th AIAA Aerospace Sciences Meeting (2012))
[23] Sitaraman, J., TIOGA: Topology independent overset grid assembly library (2015), Overset Connectivity Library for CFD
[24] Sitaraman, J.; Floros, M.; Wissink, A.; Potsdam, M., Parallel domain connectivity algorithm for unsteady flow computations using overlapping and adaptive grids, J. Comput. Phys., 229, 4703-4720 (2010) · Zbl 1305.76058
[25] Noack, R. W., A direct cut approach for overset hole cutting, (18th AIAA Computational Fluid Dynamics Conference (2007))
[26] Bonet, J.; Peraire, J., An alternating digital tree algorithm for 3d geometric searching and intersection problems, Int. J. Numer. Methods Eng., 31, 1, 1-17 (1991) · Zbl 0825.73958
[27] Lee, Y.; Baeder, J. D., Implicit hole cutting—a new approach to overset grid connectivity, (16th AIAA Computational Fluid Dynamics Conference (2003))
[28] Roget, B.; Sitaraman, J., Robust and efficient overset grid assembly for partitioned unstructured meshes, J. Comput. Phys., 260, 1-24 (2014) · Zbl 1349.65669
[29] Möller, T., A fast triangle-triangle intersection test, J. Graph. Tools, 2, 2, 25-30 (1997)
[30] Soni, K.; Chandar, D. D.; Sitaraman, J., Development of an overset grid computational fluid dynamics solver on graphical processing units, Comput. Fluids, 58, 1-14 (2011) · Zbl 1365.76242
[31] Yamamoto, Y.; Nagai, S.; Koyama, T.; Tsuda, S.; Hirabayashi, N.; Hozumi, K., CFD analysis and wind tunnel experiments of hypersonic shock-shock interaction heating for two hemi sphere cylinder problem, (40th AIAA Aerospace Sciences Meeting & Exhibit (2002)), AIAA 2002-0127
[32] Karypis, G.; Kumar, V., A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput., 20, 1, 359-392 (1998) · Zbl 0915.68129
[33] Kennedy, C. A.; Carpenter, M. H.; Lewis, R. M., Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations, Appl. Numer. Math., 35, 3, 177-219 (2000) · Zbl 0986.76060
[34] Butcher, J. C., Numerical Methods for Ordinary Differential Equations (2016), Wiley · Zbl 1354.65004
[35] van Rees, W. M.; Leonard, A.; Pullin, D.; Koumoutsakos, P., A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers, J. Comput. Phys., 230, 2794-2805 (2011) · Zbl 1316.76066
[36] 2nd International Workshop on High-Order CFD Methods, 2013.; 2nd International Workshop on High-Order CFD Methods, 2013.
[37] 4th International Workshop on High-Order CFD Methods, 2016.; 4th International Workshop on High-Order CFD Methods, 2016.
[38] Bearman, P. W.; Harvey, J. K., Golf ball aerodynamics, Aeronaut. Q., 27, 112-122 (1976)
[39] Mehta, R. D., Aerodynamics of sports balls, Annu. Rev. Fluid Mech., 17, 151-189 (1985)
[40] Aoki, K.; Muto, K.; Okanaga, H., Aerodynamic characteristics and flow pattern of a golf ball with rotation, Proc. Eng., 2, 2, 2431-2436 (2010)
[41] Muto, M.; Tsubokura, M.; Oshima, N., Negative magnus lift on a rotating sphere at around the critical Reynolds number, Phys. Fluids, 24, Article 014102 pp. (2012)
[42] Choi, J.; Jeon, W.-P.; Choi, H., Mechanism of drag reduction by dimples on a sphere, Phys. Fluids, 18, Article 041702 pp. (2006)
[43] Ting, L. L., Application of cfd technology analyzing the three-dimensional aerodynamic behavior of dimpled golf balls, (ASME International Mechanical Engineering Congress & Exposition (2002))
[44] Ting, L. L., Effects of dimple size and depth on golf ball aerodynamics, (4th ASME/JSME Joint Fluids Engineering Conference (2003))
[45] Li, J.; Tsubokura, M.; Tsunoda, M., Numerical investigation of the flow around a golf ball at around the critical Reynolds number and its comparison with a smooth sphere, Flow Turbul. Combust., 95, 415-436 (2015)
[46] Smith, C. E.; Beratlis, N.; Balaras, E.; Squires, K.; Tsunoda, M., Numerical investigation of the flow over a golf ball in the subcritical and supercritical regimes, Int. J. Heat Fluid Flow, 31, 262-273 (2010)
[47] Chowdhury, H.; Loganathan, B.; Wang, Y.; Mustary, I.; Alam, F., A study of dimple characteristics on golf ball drag, Proc. Eng., 147, 87-91 (2016)
[48] Eiseman, P. R.; Ebenezer, S. J.; Sudharshanam, V.; Anbumani, V., Gridpro manuals (2017), downloadable from
[49] Hindenlang, F.; Bolemann, T.; Munz, C.-D., Mesh curving techniques for high order discontinuous Galerkin simulations, (IDIHOM: Industrialization of High-Order Methods—A Top-Down Approach (2015), Springer), 133-152
[50] Witherden, F. D.; Farrington, A. M.; Vincent, P. E., PyFR: an open source framework for solving advection-diffusion type problems on streaming architectures using the flux reconstruction approach, Comput. Phys. Commun., 185, 3028-3040 (2014) · Zbl 1348.65005
[51] Geuzaine, C.; Remacle, J.-F., Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Eng. (Mesh-Generation Software), 79, 11, 1309-1331 (2009) · Zbl 1176.74181
[52] Witherden, F.; Vermeire, B.; Vincent, P., Heterogeneous computing on mixed unstructured grids with PyFR, Comput. Fluids, 120, 173-186 (2015) · Zbl 1390.76014
[53] Wozniak, B. D.; Witherden, F. D.; Russell, F. P.; Vincent, P. E.; Kelly, P. H., GiMMiK: generating bespoke matrix multiplication kernels for accelerators: application to high-order computational fluid dynamics, Comput. Phys. Commun., 202, 12-22 (2016)
[54] Romero, J. D., On the Development of the Direct Flux Reconstruction Scheme for High-Order Fluid Flow Simulations (2017), Stanford University, Ph.D. Thesis
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.