Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation. (English) Zbl 1391.76587
Summary: The development of a parallel immersed boundary solver for flows with complex geometries is presented. The numerical method for incompressible Navier-Stokes equations is based on the discrete stream-function formulation and unstructured Cartesian grid framework. The code parallelization is achieved by using the domain decomposition (DD) approach and Single Program Multiple Data (SPMD) programming paradigm, with the data communication among processes via the MPI protocol. A ’gathering and scattering’ strategy is used to handle the force computing on the immersed boundaries. Three tests, 3D lid-driven cavity flow, sedimentation of spheres in a container and flow through and around a circular array of cylinders are performed to evaluate the parallel efficiency of the code. The speedups obtained in these tests on a workstation cluster are reasonably good for the problem size up to 10 million and the number of processes in the range of 16-2048.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
Keywords:
parallelization; domain decomposition; massage passing interface; immersed boundary method; discrete stream-function formulationReferences:
| [1] | Peskin, C. S., The immersed boundary method, Acta Numer, 11, 479-517, (2002) · Zbl 1123.74309 |
| [2] | Mittal, R.; Iaccarino, G., Immersed boundary methods, Annu Rev Fluid Mech, 37, 239-261, (2005) · Zbl 1117.76049 |
| [3] | De Tullio, M. D.; De Palma, P.; Iaccarino, G.; Pascazio, G.; Napolitano, M., An immersed boundary method for compressible flows using local grid refinement, J Comput Phys, 225, 2098-2117, (2007) · Zbl 1118.76043 |
| [4] | You, D.; Mittal, R.; Wang, M.; Moin, P., Computational methodology for large-eddy simulation of tip-clearance flows, AIAA J, 42, 271-279, (2004) |
| [5] | Borazjani, I.; Ge, L.; Sotiropoulos, F., Curvilinear immersed boundary method for simulating fluid structure interaction with complex 3D rigid bodies, J Comput Phys, 227, 7587-7620, (2008) · Zbl 1213.76129 |
| [6] | Kang, S.; Iaccarino, G.; Ham, F.; Moin, P., Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method, J Comput Phys, 228, 6753-6772, (2009) · Zbl 1261.76032 |
| [7] | Tai, C. H.; Zhao, Y., Parallel unsteady incompressible viscous flow computations using an unstructured multigrid method, J Comput Phys, 192, 277-311, (2003) · Zbl 1047.76540 |
| [8] | Grismer, M. J.; Strang, W. Z.; Tomaro, R. F.; Witzeman, F. C., Cobalt: a parallel, implicit, unstructured Euler/Navier-Stokes solver, Adv Eng Softw, 29, 365-373, (1998) |
| [9] | Karimian, S. A.M.; Straatman, A. G., Discretization and parallel performance of an unstructured finite volume Navier-Stokes solver, Int J Numer Meth Fluids, 52, 591-615, (2006) · Zbl 1105.76039 |
| [10] | Mavriplis, D.; Pirzadeh, S., Large-scale parallel unstructured mesh computations for 3D high-lift analysis, AIAA J Aircraft, 36, 987-998, (1999) |
| [11] | Ramamurti, R.; Lohner, R., A parallel implicit incompressible flow solver using unstructured meshes, Comput Fluids, 5, 119-132, (1996) · Zbl 0866.76046 |
| [12] | Gropp, W. D.; Kaushik, D. K.; Keyes, D. E.; Smith, B. F., High-performance parallel implicit CFD, Parallel Comput, 27, 337-362, (2001) · Zbl 0971.68191 |
| [13] | Aumann, P.; Barnewitz, H.; Schwarten, H.; Becker, K.; Heinrich, R.; Roll, B., MEGAFLOW, parallel complete aircraft CFD, Parallel Comput, 27, 415-440, (2001) · Zbl 0971.68192 |
| [14] | Dolean, V.; Lanteri, S., Parallel multigrid methods for the calculation of unsteady flows on unstructured grids: algorithmic aspect and parallel performances on clusters of pcs, Parallel Comput, 30, 503-525, (2004) |
| [15] | Koubogiannis, D. G.; Poussoulidis, L. C.; Rovas, D. V.; Giannakoglou, K. C., Solution of flow problems using unstructured grids on distributed memory platforms, Comput Method Appl Mech Eng, 160, 89-100, (1998) · Zbl 0940.76041 |
| [16] | Uhlmann M. Simulation of particulate flows on multi-processor machines with distributed memory. CIEMAT technical report no. 1039, Madrid, Spain, ISSN 1135-9420; 2003. |
| [17] | Wang, Z. L.; Fan, J. R.; Luo, K., Parallel computing strategy for the simulation of particulate flows with immersed boundary method, Sci China Ser E - Tech Sci, 51, 1169-1176, (2008) · Zbl 1143.76049 |
| [18] | Wang, S. Z.; Zhang, X., An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows, J Comput Phys, 230, 3479-3499, (2011) · Zbl 1316.76083 |
| [19] | Chang, W.; Giraldo, F.; Perot, B., Analysis of an exact fractional step method, J Comput Phys, 180, 183-199, (2002) · Zbl 1130.76394 |
| [20] | Karypis G, Kumar V. METIS: a software package for partitioning unstructured graphs, partitioning meshes, and computing fill-reducing orderings of sparse matrices. METIS user’s manual (version 4.0); 1998. |
| [21] | Su, S. W.; Lai, M. C.; Lin, C. A., An immersed boundary technique for simulating complex flows with rigid boundary, Comput Fluids, 36, 313-324, (2007) · Zbl 1177.76299 |
| [22] | Perot, B.; Nallapati, R., A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows, J Comput Phys, 184, 192-214, (2003) · Zbl 1118.76307 |
| [23] | Karypis, G.; Kumar, V., A fast and high quality scheme for partitioning irregular graphs, SIAM J Sci Comput, 20, 259-392, (1999) · Zbl 0915.68129 |
| [24] | Ghia, U.; Ghia, K. N.; Shin, C. T., High-re solutions for incompressible flows using the Navier-Stokes equations and a multigrid method, J Comput Phys, 48, 387-411, (1982) · Zbl 0511.76031 |
| [25] | Bosshard, C.; Bouffanais, R.; Deville, M.; Gruber, R.; Latt, J., Computational performance of a parallelized three-dimensional high-order spectral element toolbox, Comput Fluids, 44, 1-8, (2011) · Zbl 1271.76223 |
| [26] | ten Cate, A.; Nieuwstad, C. H.; Derksen, J. J.; van den Akker, H. E.A., Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity, Phys Fluids, 14, 4012-4025, (2002) · Zbl 1185.76073 |
| [27] | Saff, E. B.; Kuijlaars, A. B.J., Distributing many points on a sphere, Math Intell, 19, 5-11, (1997) · Zbl 0901.11028 |
| [28] | Breugem WP. A combined soft-sphere collision/immersed boundary method for resolved simulations of particulate flows. In: Proceedings of the ASME 2010 Third joint US-European fluids engineering summer meeting, Montreal, Quebec, Canada, 1-5 August 2010 (FEDSM-ICNMM2010-30634). |
| [29] | Feng, Z. G.; Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J Comput Phys, 220, 20-51, (2005) · Zbl 1076.76568 |
| [30] | Uhlmann, M., An immersed boundary method with direct forcing for the simulation of particulate flows, J Comput Phys, 209, 448-476, (2005) · Zbl 1138.76398 |
| [31] | Nicolle, A.; Eames, I., Numerical study of flow through and around a circular array of cylinders, J Fluid Mech, 679, 1-31, (2011) · Zbl 1241.76146 |
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.
