The nested block preconditioning technique for the incompressible Navier–Stokes equations with emphasis on hemodynamic simulations

Ju, Liu; Yang, Weiguang; Dong, Melody; Marsden, Alison L.

doi:10.1016/j.cma.2020.113122

Cited by 25 publications

(26 citation statements)

References 70 publications

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“…With Scheme‐2, we can also conveniently address the proper temporal treatment of the traction coupling condition in geometric multiscale simulations. More specifically, the pressure on the interface between the three‐dimensional and reduced models should be collocated at the intermediate time step 19‐21 rather than at t n + 1 22 . As we observed numerically, the latter approach may further degrade the velocity temporal accuracy from second‐ to first‐order.…”

Section: Discussionmentioning

confidence: 99%

“…We also note that ∞ = 0.5 is commonly adopted as a balanced choice for CFD and FSI investigations. 6,20,32,35,36 Remark 2. One may introduce an additional set of parameters p m , p f , and p for the pressure variable (see p. 89 of Reference 11).…”

Section: The Generalized-schemes Under Comparisonmentioning

confidence: 99%

“…It sometimes yields favorable numerical performance in flow simulations 3 and presents the only scenario in which Scheme‐1 and Scheme‐2 become identical. We also note that ϱ ∞ = 0.5 is commonly adopted as a balanced choice for CFD and FSI investigations 6,20,32,35,36 …”

Section: Governing Equations and The Spatiotemporal Discretizationmentioning

confidence: 99%

“…On the outflow boundary, the coupling between dimensionally heterogeneous models is typically performed with a traction boundary condition via Dirichlet‐to‐Neumann mapping. Treating the boundary traction term with the generalized‐

α

scheme is a natural choice and is exactly the approach adopted in References 19‐21. On the other hand, the boundary traction is often represented by the downstream pressure alone, because the viscous shear stress is often several orders of magnitude smaller than the pressure.…”

Section: Introductionmentioning

confidence: 99%

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A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations

Lan

Tikenogullari

et al. 2020

Numerical Meth Engineering

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We investigate the temporal accuracy of two generalized-schemes for the incompressible Navier-Stokes equations. In a widely-adopted approach, the pressure is collocated at the time step t n + 1 while the remainder of the Navier-Stokes equations is discretized following the generalized-scheme. That scheme has been claimed to be second-order accurate in time. We developed a suite of numerical code using inf-sup stable higher-order non-uniform rational B-spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve high spatial accuracy and to investigate asymptotic temporal convergence behavior. Numerical evidence suggests that only first-order accuracy is achieved, at least for the pressure, in this aforesaid temporal discretization approach. On the other hand, evaluating the pressure at the intermediate time step t n+ f recovers second-order accuracy, and the numerical implementation is simplified. We recommend this second approach as the generalized-scheme of choice when integrating the incompressible Navier-Stokes equations.

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Section: Discussionmentioning

confidence: 99%

Section: The Generalized-schemes Under Comparisonmentioning

confidence: 99%

Section: Governing Equations and The Spatiotemporal Discretizationmentioning

confidence: 99%

α

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations

Lan

Tikenogullari

et al. 2020

Numerical Meth Engineering

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“…Then, we address the ill-conditioning issues stemming from our choice of super-penalty parameters. We adapt the block preconditioner based on an inexact Schur complement reduction (SCR) introduced in [27,28] and we combine it with a preconditioner tailored to the isogeometric discretization of the Kirchhoff plate, where we exploit the tensor product structure of B-splines and an efficient algorithm for the solution of the arising Sylvester-like system; for a detailed derivation we refer to [30,31,37]. Finally, we show through several numerical benchmarks the optimal convergence properties of the presented methodology, where our approach does not suffer from boundary locking, especially on very coarse meshes.…”

Section: Introductionmentioning

confidence: 99%

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

2021

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This work focuses on the development of a super-penalty strategy based on the $$L^2$$ L 2 -projection of suitable coupling terms to achieve $$C^1$$ C 1 -continuity between non-conforming multi-patch isogeometric Kirchhoff plates. In particular, the choice of penalty parameters is driven by the underlying perturbed saddle point problem from which the Lagrange multipliers are eliminated and is performed to guarantee the optimal accuracy of the method. Moreover, by construction, the method does not suffer from boundary locking, especially on very coarse meshes. We demonstrate the applicability of the proposed coupling algorithm to Kirchhoff plates by studying several benchmark examples discretized by non-conforming meshes. In all cases, we recover the optimal rates of convergence achievable by B-splines where we achieve a substantial gain in accuracy per degree-of-freedom compared to other choices of the penalty parameters.

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A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

Nardean

Ferronato

Abushaikha

2021

Comp and Math Methods

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In this work, we present an original block preconditioner to improve the convergence of Krylov solvers for the simulation of two-phase flow in porous media. In our modeling approach, the set of coupled governing equations is addressed in a fully implicit fashion, where Darcy's law and mass conservation are discretized in an original way by combining the mixed hybrid finite element (MHFE) and the finite volume (FV) methods. The solution to the sequence of large-size nonsymmetric linearized systems of equations that stem during a full-transient simulation represents the most time and resource consuming task, thus motivating the need for efficient preconditioned Krylov solvers. The proposed preconditioner exploits the block structure of the Jacobian matrix while coping with the nonsymmetric nature of the individual blocks. Both academic and realistic applications have been used to challenge the preconditioner, allowing to point out its robustness, stability and overall computational efficiency.

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The nested block preconditioning technique for the incompressible Navier–Stokes equations with emphasis on hemodynamic simulations

Cited by 25 publications

References 70 publications

A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations

A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations

A projected super-penalty method for the $$C^1$$-coupling of multi-patch isogeometric Kirchhoff plates

A block preconditioner for two‐phase flow in porous media by mixed hybrid finite elements

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