Abstract
In this paper, computational algorithms for the Stokes-Biot coupled system are proposed to study the interaction of a free fluid with a poroelastic material. The decoupling strategy we employ is to cast the coupled fluid-poroelastic system as a constrained optimization problem with a Neumann type control that enforces continuity of the normal components of the stress on the interface. The optimization objective is to minimize any violation of the other interface conditions. Two numerical algorithms based on a residual updating technique are presented. One solves a least squares problem and the other solves a linear problem when the fluid velocity in the poroelastic structure is smooth enough. Both algorithms yield the minimizer of the constrained optimization problem. Some numerical results are provided to validate the accuracy and efficiency of the proposed algorithms.
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Acknowledgments
This work was supported by the Institute for Mathematics and its Applications (IMA), which is funded by the National Science Foundation (NSF). A. Cesmelioglu would like to thank Oakland University for the URC Faculty Research Fellowship Award. H. Lee was supported by NSF under contract number DMS 1418960 and A. Quaini’s research was supported in part by NSF under grant DMS-1262385. The research of S.-Y. Yi was supported by NSF under contract number DMS 1217123.
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Cesmelioglu, A., Lee, H., Quaini, A., Wang, K., Yi, SY. (2016). Optimization-Based Decoupling Algorithms for a Fluid-Poroelastic System. In: Brenner, S. (eds) Topics in Numerical Partial Differential Equations and Scientific Computing. The IMA Volumes in Mathematics and its Applications, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6399-7_4
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DOI: https://doi.org/10.1007/978-1-4939-6399-7_4
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