Optimization-Based Decoupling Algorithms for a Fluid-Poroelastic System

Çeşmelioǧlu, Ayçıl; Lee, Hyesuk; Quaini, Annalisa; Wang, Kening; Yi, Son-Young

doi:10.1007/978-1-4939-6399-7_4

Cited by 11 publications

(18 citation statements)

References 15 publications

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“…We let v = u m , ξ =η m , r = p m in the Galerkin formulation (GF). Then the Cauch-Schwarz inequality, inequalities (7), (10), (12), (13), (14) and assumption (16) on K imply (after neglecting the β term which is nonnegative)…”

Section: Proof Of (34)mentioning

confidence: 99%

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Analysis of the coupled Navier–Stokes/Biot problem

Çeşmelioǧlu

2017

Journal of Mathematical Analysis and Applications

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Section: Proof Of (34)mentioning

confidence: 99%

“…We let v =u m , r =ṗ m and ξ =η m in the above, use the Cauch-Schwarz inequality, assumption (44), inequalities (7), (10), (12), (13), (14) and assumption (16) on K to get (neglecting the nonnegative β term)…”

mentioning

confidence: 99%

Analysis of the coupled Navier–Stokes/Biot problem

Çeşmelioǧlu

2017

Journal of Mathematical Analysis and Applications

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“…Several approaches exist for decoupling systems of equations, permitting use of partitioned solvers, which may be more attractive and allow the use of legacy codes . This allows operations on a smaller system of matrix for each subsystem.…”

Section: Introductionmentioning

confidence: 99%

“…The FSI problem was formulated as a constrained optimization problem, where the jump in velocities of the fluid and the elastic structure is minimized by a Neumann control enforcing the continuity of stress on the interface. This method was extended to the Stokes‐Biot system, where the stress force along the interface is utilized to minimize the mismatch of two interface conditions: the balance of normal velocities and the Beavers‐Joseph‐Saffman condition. In the approach, the subproblems are discretized in time based on the backward Euler method and the structure velocity in interface conditions is approximated by the first‐order finite difference; therefore, the overall accuracy in time is

𝒪 (Δ t)

.…”

Section: Introductionmentioning

confidence: 99%

“…The objective of this work is to develop a decoupling algorithm for a nonlinear Stokes‐Biot system based on second‐order temporal discretization schemes. The method for decoupling is similar to the one in Reference ; however, the accuracy in time is improved for the fluid and poroelastic subproblems and also for the interface conditions. The nonlinear Stokes problem is discretized by the Crank‐Nicolson method with linear extrapolation and the Biot system is discretized by the combination of Crank‐Nicolson and the second‐order Newmark scheme.…”

Section: Introductionmentioning

confidence: 99%

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Second‐order time discretization for a coupled quasi‐Newtonian fluid‐poroelastic system

Kunwar

Lee

Seelman

2019

Numerical Methods in Fluids

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Numerical methods are proposed for the nonlinear Stokes-Biot system modeling interaction of a free fluid with a poroelastic structure. We discuss time discretization and decoupling schemes that allow the fluid and the poroelastic structure computed independently using a common stress force along the interface. The coupled system of nonlinear Stokes and Biot is formulated as a least-squares problem with constraints, where the objective functional measures violation of some interface conditions. The local constraints, the Stokes and Biot models, are discretized in time using second-order schemes. Computational algorithms for the least-squares problems are discussed and numerical results are provided to compare the accuracy and efficiency of the algorithms. K E Y W O R D Sdomain decomposition, fluid structure interaction, poroelasticity INTRODUCTIONThe interaction of a fluid with a poroelastic material is of great importance in many engineering and biological applications. In such applications, a free fluid interacts with a deformable porous medium, where the structure is poroelastic, accounting for both the effects of porosity and elasticity. These interactions can be found in many applications such as reservoir engineering, groundwater flow, blood flow through vessels, and more. 1-4 Specifically for a blood flow, the interaction between blood and the arteries, as well as the effect of a blood clot, is a fluid-poroelastic system. 2 Other related applications are fluid flows through aquifers, bodies of permeable rock that can contain or transmit groundwater, where fluids such as water or oil flow through materials such as clay, sand, or sandstone. 3,5 There are a wide variety of solution algorithms proposed for fluid-structure interaction (FSI) problems of the Navier-Stokes coupled with the linear elasticity, but each is limited by computational complexity and stability. [6][7][8] While studies on the system of fluid and elastic structure have been active for the last 20 years, interaction of fluid flows with a poroelastic structure has received less attention and there are relatively a few numerical results reported for such problems. FSI problems involving an incompressible fluid and a poroelastic structure are often represented by the coupled Navier-Stokes and Biot (or Stokes-Biot) system with conditions on the interface between fluid and structure subdomains. A monolithic approach is computationally complex as it requires solving a large linear system; therefore, one needs the development of efficient and appropriate preconditioners for the discretized linear system. Ambartsumyan et al 9 studied a monolithic scheme for the Stokes equations coupled with the quasi-static Biot system, based on the Lagrange multiplier method. The proposed monolithic scheme was analyzed for stability and error estimation. Recently, a nonlinear Stokes-Biot system was considered for the analysis of well-posedness in Reference 10, Int J Numer Meth Fluids. 2020;92:687-702.wileyonlinelibrary.com/journal/fld Consider the domain of a fluid-...

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Numerical analysis of the coupling of free fluid with a poroelastic material

Çeşmelioǧlu

Chidyagwai

2019

Numerical Methods Partial

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This paper presents a numerical solution of the coupled system of the time‐dependent Stokes and fully dynamic Biot equations. The numerical scheme is based on standard inf‐sup stable finite elements in space and the Backward Euler scheme in time. We establish stability of the scheme and derive error estimates for the fully discrete coupled scheme. To handle realistic parameters which may cause nonphysical oscillations in the pore fluid pressure, a heuristic stabilization technique is considered. Numerical errors and convergence rates for smooth problems as well as tests on realistic material parameters are presented.

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Optimization-Based Decoupling Algorithms for a Fluid-Poroelastic System

Cited by 11 publications

References 15 publications

Analysis of the coupled Navier–Stokes/Biot problem

Analysis of the coupled Navier–Stokes/Biot problem

Second‐order time discretization for a coupled quasi‐Newtonian fluid‐poroelastic system

Numerical analysis of the coupling of free fluid with a poroelastic material

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