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Abstract This work focuses on modeling the interaction between an incompressible, viscous fluid and a poroviscoelastic material. The fluid flow is described using the time‐dependent Stokes equations, and the poroelastic material using the Biot model. The viscoelasticity is incorporated in the equations using a linear Kelvin–Voigt model. We introduce two novel, noniterative, partitioned numerical schemes for the coupled problem. The first method uses the second‐order backward differentiation formula (BDF2) for implicit integration, while treating the interface terms explicitly using a second‐order extrapolation formula. The second method is the Crank–Nicolson and Leap‐Frog (CNLF) method, where the Crank–Nicolson method is used to implicitly advance the solution in time, while the coupling terms are explicitly approximated by the Leap‐Frog integration. We show that the BDF2 method is unconditionally stable and uniformly stable in time, while the CNLF method is stable under a CFL condition. Both schemes are validated using numerical simulations. Second‐order convergence in time is observed for both methods. Simulations over a longer period of time show that the errors in the solution remain bounded. Cases when the structure is poroviscoelastic and poroelastic are included in numerical examples. 

Determination of abdominal aortic aneurysm (AAA) rupture risk involves the accurate prediction of mechanical stresses acting on the arterial tissue, as well as the wall strength which has a correlation with oxygen supply within the aneurysmal wall. Our laboratory has previously reported the significance of an intraluminal thrombus (ILT) presence and morphology on localized oxygen deprivation by assuming a uniform consistency of ILT. The aim of this work is to investigate the effects of ILT structural composition on oxygen flow by adopting a multilayered porous framework and comparing a two-layer ILT model with one-layer models. Three-dimensional idealized and patient-specific AAA geometries are generated. Numerical simulations of coupled fluid flow and oxygen transport between blood, arterial wall, and ILT are performed, and spatial variations of oxygen concentrations within the AAA are obtained. A parametric study is conducted, and ILT permeability and oxygen diffusivity parameters are individually varied within a physiological range. A gradient of permeability is also defined to represent the heterogenous structure of ILT. Results for oxygen measures as well as filtration velocities are obtained, and it is found that the presence of any ILT reduces and redistributes the concentrations in the aortic wall markedly. Moreover, it is found that the integration of a porous ILT significantly affects the oxygen transport in AAA and the concentrations are linked to ILT’s permeability values. Regardless of the ILT stratification, maximum variation in wall oxygen concentrations is higher in models with lower permeability, while the concentrations are not sensitive to the value of the diffusion coefficient. Based on the observations, we infer that average one-layer parameters for ILT material characteristics can be used to reasonably estimate the wall oxygen concentrations in aneurysm models. 

We present an extension of a non-iterative, partitioned method previously designed and used to model the interaction between an incompressible, viscous fluid and a thick elastic structure. The original method is based on the Robin boundary conditions and it features easy implementation and unconditional stability. However, it is sub-optimally accurate in time, yielding only O(Δt12) rate of convergence. In this work, we propose an extension of the method designed to improve the sub-optimal accuracy. We analyze the stability properties of the proposed method, showing that the method is stable under certain conditions. The accuracy and stability of the method are computationally investigated, showing a significant improvement in the accuracy when compared to the original scheme, and excellent stability properties. Furthermore, since the method depends on a combination parameter used in the Robin boundary conditions, whose values are problem specific, we suggest and investigate formulas according to which this parameter can be determined.