An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure

Bukač, Martina; Yotov, Ivan; Zunino, Paolo

doi:10.1002/num.21936

Cited by 62 publications

(54 citation statements)

References 82 publications

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“…We assume that all the finite element approximation spaces comply with the prescribed Dirichlet conditions on external boundaries BΩ f , BΩ p , without entering into the details of all possible variations for cases (i) and (ii). The bilinear forms relative to the structure, namely equation (5), are: For the free flow, equations (1)- (2), and the filtration through the porous matrix, equations (6)-(7), the bilinear forms are:…”

Section: Finite Element Approximation Of the Coupled Problem Using Nimentioning

confidence: 99%

“…In the context of biomedical applications, FSI studies involving poroelastic materials are scanty. Among the available contributions, we mention [1,39], as well as our recent work [5].…”

Section: Introductionmentioning

confidence: 99%

“…The Nitsche's coupling approach allows for treating the mixed form of Darcy flow and thus provides accurate approximation to the filtration velocity. This is an alternative to the Lie-splitting scheme developed in [5], which is suitable for the pressure formulation of Darcy flow.…”

Section: Introductionmentioning

confidence: 99%

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Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche’s coupling approach

Bukač

Yotov

Zakerzadeh

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand, it shares common traits with fluid-structure interaction. On the other hand it resembles the Stokes-Darcy coupling. For these reasons, the numerical simulation of the Stokes-Biot coupled system is a challenging task. The need of large memory storage and the difficulty to characterize appropriate solvers and related preconditioners for the equations at hand are typical shortcomings of classical discretization methods applied to this problem, such as the finite element method for spatial discretization and finite differences for time stepping. The application of loosely coupled time advancing schemes mitigates these issues, because it allows to solve each equation of the system independently with respect to the others, at each time step. In this work, we develop and thoroughly analyze a loosely coupled scheme for Stokes-Biot equations. The scheme is based on Nitsche's method for enforcing interface conditions. Once the interface operators corresponding to the interface conditions have been defined, time lagging allows us to build up a loosely coupled scheme with good stability properties. The stability of the scheme is guaranteed provided that appropriate stabilization operators are introduced into the variational formulation of each subproblem. The error of the resulting method is also analyzed, showing that splitting the equations pollutes the optimal approximation properties of the underlying discretization schemes. In order to restore good approximation properties, while maintaining the computational efficiency of the loosely coupled approach, we consider the application of the loosely coupled scheme as a preconditioner for the monolithic approach. Both theoretical insight and numerical results confirm that this is a promising way to develop efficient solvers for the problem at hand.

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Section: Finite Element Approximation Of the Coupled Problem Using Nimentioning

confidence: 99%

“…In the context of biomedical applications, FSI studies involving poroelastic materials are scanty. Among the available contributions, we mention [1,39], as well as our recent work [5].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche’s coupling approach

Bukač

Yotov

Zakerzadeh

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…To approximate the horizontal displacement, we need to use the conservation of momentum (8) and the no-slip interface condition (9). Thus, by applying (8) and (9) at the location denoted by e in Fig.…”

Section: Discretization For V P and V F At The Interfacementioning

confidence: 99%

“…Following the same technique to approximate the components of the stress tensor as above, we again obtain a formulation can be calculated from the interface conditions (8) and (9). By applying these expressions to (20), the unknowns for both subproblems are included in the coupling between the two systems.…”

Section: Discretization For V P and V F At The Interfacementioning

confidence: 99%

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

Luo

Rodrigo

Gaspar

et al. 2018

Journal of Computational Physics

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The interaction between fluid flow and a deformable porous medium is a complicated multi-physics problem, which can be described by a coupled model based on the Stokes and poroelastic equations. A monolithic multigrid method together with either a coupled Vanka smoother or a decoupled Uzawa smoother is employed as an efficient numerical technique for the linear discrete system obtained by finite volumes on staggered grids. A specialty in our modeling approach is that at the interface of the fluid and poroelastic medium, two unknowns from the different subsystems are defined at the same grid point. We propose a special discretization at and near the points on the interface, which combines the approximation of the governing equations and the considered interface conditions. In the decoupled Uzawa smoother, Local Fourier Analysis (LFA) helps us to select optimal values of the relaxation parameter appearing. To implement the monolithic multigrid method, grid partitioning is used to deal with the interface updates when communication is required between two subdomains. Numerical experiments show that the proposed numerical method has an excellent convergence rate. The efficiency and robustness of the method are confirmed in numerical experiments with typically small realistic values of the physical coefficients.

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Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

Avalos,

Gurvich,

Webster

2024

Math Methods in App Sciences

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A filtration system comprising a Biot poroelastic solid coupled to an incompressible Stokes free‐flow is considered in 3D. Across the flat 2D interface, the Beavers‐Joseph‐Saffman coupling conditions are taken. In the inertial, linear, and non‐degenerate case, the hyperbolic‐parabolic coupled problem is posed through a dynamics operator on a chosen energy space, adapted from Stokes‐Lamé coupled dynamics. A semigroup approach is utilized to circumvent issues associated to mismatched trace regularities at the interface. The generation of a strongly continuous semigroup for the dynamics operator is obtained via a non‐standard maximality argument. The latter employs a mixed‐variational formulation in order to invoke the Babuška‐Brezzi theorem. The Lumer‐Philips theorem then yields semigroup generation, and thereby, strong and generalized solutions are obtained. For the linear dynamics, density obtains the existence of weak solutions; we extend to the case where the Biot compressibility of constituents degenerates. Thus, for the inertial linear Biot‐Stokes filtration system, we provide a clear elucidation of strong solutions and a construction of weak solutions, as well as their regularity through associated estimates.

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An operator splitting approach for the interaction between a fluid and a multilayered poroelastic structure

Cited by 62 publications

References 82 publications

Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche’s coupling approach

Partitioning strategies for the interaction of a fluid with a poroelastic material based on a Nitsche’s coupling approach

Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system

Weak and strong solutions for a fluid‐poroelastic‐structure interaction via a semigroup approach

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