Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation
KAUST DepartmentExtreme Computing Research Center
Online Publication Date2018-07-19
Print Publication Date2018-12
Permanent link to this recordhttp://hdl.handle.net/10754/628810
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AbstractImmersed boundary (IB) methods deal with incompressible visco-elastic solids interacting with incompressible viscous fluids. A long-standing issue of IB methods is the challenge of accurately imposing the incompressibility constraint at the discrete level. We present the divergence-conforming immersed boundary (DCIB) method to tackle this issue. The DCIB method leads to completely negligible incompressibility errors at the Eulerian level and various orders of magnitude of increased accuracy at the Lagrangian level compared to other IB methods. Furthermore, second-order convergence of the incompressibility error at the Lagrangian level is obtained as the discretization is refined. In the DCIB method, the Eulerian velocity–pressure pair is discretized using divergence-conforming B-splines, leading to inf–sup stable and pointwise divergence-free Eulerian solutions. The Lagrangian displacement is discretized using non-uniform rational B-splines, which enables to robustly handle large mesh distortions. The data transfer needed between the Eulerian and Lagrangian descriptions is performed at the quadrature level using the same spline basis functions that define the computational meshes. This conduces to a fully variational formulation, sharp treatment of the fluid–solid interface, and a 0.5 increase in the convergence rate of the Eulerian velocity and the Lagrangian displacement measured in L2 norm in comparison with using discretized Dirac delta functions for the data transfer. By combining the generalized-α method and a block-iterative solution strategy, the DCIB method results in a fully-implicit discretization, which enables to take larger time steps. Various two- and three-dimensional problems are solved to show all the aforementioned properties of the DCIB method along with mesh-independence studies, verification of the numerical method by comparison with the literature, and measurement of convergence rates.
CitationCasquero H, Zhang YJ, Bona-Casas C, Dalcin L, Gomez H (2018) Non-body-fitted fluid–structure interaction: Divergence-conforming B-splines, fully-implicit dynamics, and variational formulation. Journal of Computational Physics 374: 625–653. Available: http://dx.doi.org/10.1016/j.jcp.2018.07.020.
SponsorsH. Casquero and Y. Zhang were supported in part by the PECASE Award N00014-16-1-2254 and NSF CAREER Award OCI-1149591. H. Gomez was partially supported by the European Research Council through the FP7 Ideas Starting Grant (project # 307201). C. Bona-Casas was supported by the Spanish Ministry of Economy and Competitiveness (MINECO/AEI/FEDER, UE) through project DPI2017-86610-P. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575. Specifically, it used the Bridges system, which is supported by NSF award number ACI-1445606, at the Pittsburgh Supercomputing Center (PSC). This work also used the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (RES-FI-2018-1-0026). Finally, we would like to thank Dr. Sugiyama for facilitating us the data that we have reproduced in this article in order to make comparisons.
JournalJournal of Computational Physics