Three-Dimensional Simulation of Stokes Flow Around a Rigid Structure Using FMM/GPU Accelerated BEM
Composite materials play an important role in aircraft, space and automotive industries, wind power industry. One of the most commonly used methods for the manufacture of composite materials is the impregnation of dry textiles by a viscous liquid binder. During the process, cavities (voids) of various sizes can be formed and then move in a liquid resin flows in the complex system of channels formed by textile fibers. The presence of such cavities results in a substantial deterioration of the mechanical properties of the composites. As a result, the development and effective implementation of the numerical methods and approaches for the effective 3D simulation of the viscous liquid flow around a rigid structure of different configuration. In the present study, the mathematical model and its effective numerical implementation for the study of hydrodynamic processes around fixed structure at low Reynolds numbers is considered. The developed approach is based on the boundary element method for 3D problems accelerated both via an advanced scalable algorithm (FMM), and via utilization of a heterogeneous computing architecture (multicore CPUs and graphics processors). This enables direct large scale simulations on a personal workstation, which is confirmed by test and demo computations. The simulation results and details of the method and accuracy/performance of the algorithm are discussed. The results of the research may be used for the solution of problems related to microfluidic device construction, theory of the composite materials production, and are of interest for computational hydrodynamics as a whole.
KeywordsStokes flow Boundary element method Fast multipole method High-performance computing GPUs
This study is supported in part by the Skoltech Partnership Program (developing and testing of the accelerated BEM version, conducting of the calculations), part of the study devoted to the problem formulation of the flow near rigid structures is carried out with the support of the grant RFBR 18-31-00074, and FMM routine is provided by Fantalgo, LLC (Maryland, USA).
- 2.Abramova, O.A., Itkulova, Y.A., Gumerov, N.A., Akhatov, I.S.: Three-dimensional simulation of the dynamics of deformable droplets of an emulsion using the boundary element method and the fast multipole method on heterogeneous computing systems. Vychislitelínye Metody i Programmirovanie 14, 438–450 (2013)Google Scholar
- 3.Abramova O.A., Itkulova Y.A., Gumerov N.A.: FMM/GPU accelerated BEM simulations of emulsion flows in microchannels. In: ASME 2013 IMECE (2013). https://doi.org/10.1115/imece2013-63193
- 4.Arcila, I.P., Power, H., Londono, C.N., Escobar, W.F.: Boundary element method for the dynamic evolution of intra-tow voids in dual-scale fibrous reinforcements using a stokes-darcy formulation. Eng. Anal. Bound. Elem. 87, 133–152 (2018). https://doi.org/10.1017/s0022112069000759MathSciNetCrossRefzbMATHGoogle Scholar
- 5.Gangloff Jr., J.J., Daniel, C., Advani, S.G.: A model of a two-phase resin and void flow during composites processing. Int. J. Multiph. Flow. 65, 51–60 (2014). https://doi.org/10.1016/j.ijmultiphaseflow.2014.05.015CrossRefGoogle Scholar
- 11.Hu, Q., Gumerov, N.A., Duraiswami, R.: Scalable fast multipole methods on distributed heterogeneous architectures. In: Proceedings of Supercomputing 2011, Seattle, Washington (2011). https://doi.org/10.1145/2063384.2063432
- 12.Hu, Q., Gumerov, N.A., Duraiswami, R.: Scalable distributed fast multipole methods. In: Proceedings of 2012 IEEE 14th International Conference on High Performance Computing and Communications, UK, Liverpool, pp. 270–279 (2012). https://doi.org/10.1109/ipdpsw.2014.110
- 13.Itkulova (Pityuk) Y.A., Abramova O.A., Gumerov N.A.: Boundary element simulations of compressible bubble dynamics in stokes flow. In: ASME 2013. IMECE2013-63200, P. V07BT08A010 (2013). https://doi.org/10.1115/imece2013-63200
- 14.Itkulova (Pityuk) Y.A., Abramova O.A., Gumerov N.A., Akhatov I.S.: Boundary element simulations of free and forced bubble oscillations in potential flow. In: Proceedings of the ASME2014 International Mechanical Engineering Congress and Exposition, vol. 7. IMECE2014-36972 (2014). https://doi.org/10.1115/IMECE2014-36972