Isogeometric divergence-conforming variational multiscale formulation of incompressible turbulent flows

Opstal, T. M. van; Yan, Jinhui; Coley, Christopher; Evans, John A.; Kvamsdal, Trond; Bazilevs, Yuri

doi:10.1016/j.cma.2016.10.015

Cited by 67 publications

(30 citation statements)

References 49 publications

(79 reference statements)

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“…Van Opstal et al. [143] recently obtained very promising results from a variational multiscale (VMS) turbulence modeling approach [144] based on div-conforming B-splines, building on the subgrid vortex approach mentioned in [66, page 272] and [145]. We anticipate that these advances can be adapted to the problem setting explored in this paper to improve the efficiency and accuracy of immersogeometric heart valve simulations.…”

Section: Conclusion and Further Workmentioning

confidence: 94%

Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

Kamensky

Hsu

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This paper uses a divergence-conforming B-spline fluid discretization to address the long-standing issue of poor mass conservation in immersed methods for computational fluid–structure interaction (FSI) that represent the influence of the structure as a forcing term in the fluid subproblem. We focus, in particular, on the immersogeometric method developed in our earlier work, analyze its convergence for linear model problems, then apply it to FSI analysis of heart valves, using divergence-conforming B-splines to discretize the fluid subproblem. Poor mass conservation can manifest as effective leakage of fluid through thin solid barriers. This leakage disrupts the qualitative behavior of FSI systems such as heart valves, which exist specifically to block flow. Divergence-conforming discretizations can enforce mass conservation exactly, avoiding this problem. To demonstrate the practical utility of immersogeometric FSI analysis with divergence-conforming B-splines, we use the methods described in this paper to construct and evaluate a computational model of an in vitro experiment that pumps water through an artificial valve.

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Section: Conclusion and Further Workmentioning

confidence: 94%

Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

Kamensky

Hsu

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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“…We begin our numerical tests with the simplest extension of the Oseen problem, namely, steady Navier-Stokes flow. We test convergence with a variant of the manufactured solution called the regularized lid-driven cavity, as proposed in [62] and studied also by [63]. In particular, we choose, a priori, the exact velocity solution from [62],…”

Section: Steady Flow: the Regularized Lid-driven Cavitymentioning

confidence: 99%

Variational multiscale modeling with discretely divergence-free subscales

Evans

Kamensky

Bazilevs

2020

Computers & Mathematics with Applications

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We introduce a residual-based stabilized formulation for incompressible Navier-Stokes flow that maintains discrete (and, for divergence-conforming methods, strong) mass conservation for inf-sup stable spaces with H 1 -conforming pressure approximation, while providing optimal convergence in the diffusive regime, robustness in the advective regime, and energetic stability. The method is formally derived using the variational multiscale (VMS) concept, but with a discrete fine-scale pressure field which is solved for alongside the coarse-scale unknowns such that the coarse and fine scale velocities separately satisfy discrete mass conservation. We show energetic stability for the full Navier-Stokes problem, and we prove convergence and robustness for a linearized model (Oseen flow), under the assumption of a divergence-conforming discretization. Numerical results indicate that all properties extend to the fully nonlinear case and that the proposed formulation can serve to model unresolved turbulence.

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“…Other recent related work includes the IGA divergence-conforming VMS method of Opstal et al in [13]. They also employ an H 1 0 -orthogonality between the velocity large-and small-scales on a local level.…”

Section: Contextmentioning

confidence: 99%

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations

Eikelder

Akkerman

2018

Computer Methods in Applied Mechanics and Engineering

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This paper presents the construction of a correct-energy stabilized finite element method for the incompressible Navier-Stokes equations. The framework of the methodology and the correct-energy concept have been developed in the convective-diffusive context in the preceding paper [M.F.P. ten Eikelder, I. Akkerman, Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. I: The convective-diffusive context, Comput. Methods Appl. Mech. Engrg. 331 (2018) 259-280]. The current work extends ideas of the preceding paper to build a stabilized method within the variational multiscale (VMS) setting which displays correct-energy behavior. Similar to the convection-diffusion case, a key ingredient is the proper dynamic and orthogonal behavior of the small-scales. This is demanded for correct energy behavior and links the VMS framework to the streamline-upwind Petrov-Galerkin (SUPG) and the Galerkin/least-squares method (GLS).The presented method is a Galerkin/least-squares formulation with dynamic divergence-free small-scales (GLSDD). It is locally mass-conservative for both the large-and small-scales separately. In addition, it locally conserves linear and angular momentum. The computations require and employ NURBS-based isogeometric analysis for the spatial discretization. The resulting formulation numerically shows improved energy behavior for turbulent flows comparing with the original VMS method.

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Isogeometric divergence-conforming variational multiscale formulation of incompressible turbulent flows

Cited by 67 publications

References 49 publications

Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

Immersogeometric cardiovascular fluid–structure interaction analysis with divergence-conforming B-splines

Variational multiscale modeling with discretely divergence-free subscales

Correct energy evolution of stabilized formulations: The relation between VMS, SUPG and GLS via dynamic orthogonal small-scales and isogeometric analysis. II: The incompressible Navier–Stokes equations

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