Research

Publications:

• Sergio Caucao, Aashi Dalal, Tongtong Li, and Ivan Yotov. Mixed finite element methods for the Navier-Stokes-Biot model. In: Ivan Lirkov, Svetozar Margenov (eds) Large-Scale Scientific Computations. 14th International Conference, LSSC 2023, Sozopol, Bulgaria, June 5–9, 2023, Revised Selected Papers. Springer, Cham. DOI: 10.1007/978-3-031-56208-2. link  pdf 

• Aashi Dalal, Rebecca Durst, Annalisa Quaini, and Ivan Yotov. A Robin-Robin splitting method for the Stokes Biot fluid-poroelastic structure interaction model. Submitted to Mathematics of Computation. Available on arXiv. link  pdf 

• Sergio Caucao, Aashi Dalal, and Ivan Yotov. A Banach space formulation for the Navier-Stokes-Biot coupled problem. Available on arXiv. link  pdf 

• Aashi Dalal, Boris Tzankov, and Ivan Yotov. A splitting method for the fully mixed formulation of the Stokes Biot fluid-poroelastic structure interaction model. In preparation. 

Figure: fluid and Darcy pressure computed by the non-iterative Robin-Robin scheme (top) and the monolithic scheme (bottom) at times t = 0.007, 0.014, 0.021 s (from left to right). 

Figure: fluid and Darcy velocity computed by the non-iterative Robin-Robin scheme (top) and the monolithic scheme (bottom) at times t = 0.007, 0.014, 0.021 s (from left to right). The arrows represent the velocity vectors and the color represents the velocity magnitudes. 

• Air flow through a filter (A Banach space formulation for the Navier-Stokes-Biot coupled problem)

Figure: Computed fluid and Darcy velocity (arrows not scaled) and their magnitudes at times t ∈ {20,80,200,400} (from top to bottom).

Figure: Computed fluid and Darcy pressure (we plot its difference from the reference pressure) at times t ∈ {20,80,200,400} (from top to bottom).