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A Higher-Order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid–Structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures

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Abstract

This manuscript presents a discontinuous Galerkin-based numerical method for solving fluid–structure interaction problems involving incompressible, viscous fluids. The fluid and structure are fully coupled via two sets of coupling conditions. The numerical approach is based on a high-order discontinuous Galerkin (with Interior Penalty) method, which is combined with the Arbitrary Lagrangian–Eulerian approach to deal with the motion of the fluid domain, which is not known a priori. Two strongly coupled partitioned schemes are considered to resolve the interaction between fluid and structure: the Dirichlet–Neumann and the Robin–Neumann schemes. The proposed numerical method is tested on a series of benchmark problems, and is applied to a fluid–structure interaction problem describing the flow of blood in a patient-specific aortic abdominal aneurysm before and after the insertion of a prosthesis known as stent graft. The proposed numerical approach provides sharp resolution of jump discontinuities in the pressure and normal stress across fluid–structure and structure–structure interfaces. It also provides a unified framework for solving fluid–structure interaction problems involving nonlinear structures, which may develop shock wave solutions that can be resolved using a unified discontinuous Galerkin-based approach.

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Acknowledgements

This research has been supported in part by the National Science Foundation under Grants DMS-1613757 (Canic), DMS-1318763 (Canic and Wang), DMS-1311709 (Canic), DMS-1263572 (Canic, Quaini and Wang), DMS-1109189 (Canic and Quaini), DMS-1620384 (Quaini). The authors acknowledge the use of the Maxwell and Opuntia Clusters and the support from the Center of Advanced Computing and Data Systems at the University of Houston to carry out the research presented here.

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  1. Department of Mathematics, University of Houston, Houston, TX, USA

    Yifan Wang, Annalisa Quaini & Sunčica Čanić

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  1. Yifan Wang
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Wang, Y., Quaini, A. & Čanić, S. A Higher-Order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid–Structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures. J Sci Comput 76, 481–520 (2018). https://doi.org/10.1007/s10915-017-0629-y

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